Analysis method of eccentric compression bearing capacity of corroded reinforced concrete column

Abstract

The present application relates to a kind of corrosion reinforced concrete column eccentric compression bearing capacity analysis method, comprising the following steps: measuring and calculating the basic parameters of eccentric compression reinforced concrete component before and after corrosion;Based on the basic parameters, the limit corrosion rate of eccentric compression concrete component is calculated, and the eccentric compression failure mode is determined;Analysis of the eccentric compression bearing capacity of the eccentric compression reinforced concrete component corresponding to different eccentric compression failure modes.Compared with the prior art, the present application is based on the stress state of the reinforcement on the side far from the axial force (i.e. far side) and the side close to the axial force (i.e. near side) in the eccentric compression column when the normal section fails, realizes the normal section bearing capacity calculation of the eccentric compression reinforced concrete component when the reinforcement on the far side and the near side is arbitrarily corroded, the highest order equation for solving is a quadratic equation, has the advantages of clear concept and simple calculation, can quickly and accurately analyze and evaluate the normal section bearing capacity of the eccentric compression reinforced concrete component.

Description

Technical Field

[0001] This invention relates to the field of civil engineering technology, and in particular to a method for analyzing the eccentric compressive bearing capacity of corroded reinforced concrete columns. Background Technology

[0002] Under the long-term influence of corrosive media in the environment, the reinforcing steel in concrete structures will corrode. This corrosion leads to the degradation of concrete structural performance and premature failure. Therefore, understanding the evolutionary laws governing the performance of concrete structures has attracted widespread attention from academic and engineering communities both domestically and internationally.

[0003] To address this, numerous scholars both domestically and internationally have explored simplified analytical methods for the cross-sectional bearing capacity of eccentrically compressed corroded reinforced concrete members. In existing methods for analyzing the cross-sectional bearing capacity of eccentrically compressed corroded reinforced concrete members, scholars generally pre-determine the degree of eccentricity to predict the stress state of the longitudinal reinforcement on the side furthest from the axial force (hereinafter referred to as the "far side," and the other side as the "near side"), thereby establishing and solving the force-moment equilibrium equations to obtain the cross-sectional bearing capacity of the eccentrically compressed corroded reinforced concrete member. That is, in the case of large eccentricity, the stress in the far-side longitudinal reinforcement in the force-moment equilibrium equations is in the tensile yielding stage; in the case of small eccentricity, the stress in the far-side longitudinal reinforcement in the force-moment equilibrium equations is in the tensile / compressive elastic stage.

[0004] However, with increasing corrosion rate, the yield / buckling stress / strain and ultimate stress / strain of the reinforcing bars decrease, and the yield plateau shortens or even disappears. This may lead to the stress in the distal longitudinal reinforcement of eccentrically compressed corroded reinforced concrete members being in a compressive elastic, yield / buckling state, or a tensile elastic, yielding, hardening, or even tensile fracture state when the members fail at the normal section. Existing analytical methods fail to consider the above-mentioned changes in the failure mode of eccentrically compressed corroded reinforced concrete members caused by steel corrosion, and lack a simplified analytical method for the normal section bearing capacity of eccentrically compressed corroded reinforced concrete members that clearly distinguishes different failure modes. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing the eccentric compressive bearing capacity of corroded reinforced concrete columns, so as to facilitate and accurately analyze the eccentric compressive bearing capacity of corroded reinforced concrete components under different failure modes.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for analyzing the eccentric compressive bearing capacity of a corroded reinforced concrete column includes the following steps:

[0008] Step 1) Measure and calculate the basic parameters of the eccentrically compressed reinforced concrete member before and after corrosion;

[0009] The basic parameters of the eccentrically compressed reinforced concrete member before and after corrosion include the initial (uncorroded) cross-sectional width. b Initial cross-section height h Initial cross-section effective height h 0. Thickness of the concrete protective layer on the far and near sides c and c' Distance from the edge of the initial section on the far and near sides to the resultant point of the longitudinal reinforcement on that side a s and a′ s Concrete strength grade, concrete compressive strength f c Concrete tensile strength f t Types of deformed or plain longitudinal reinforcement and stirrups; average corrosion rate of distal and proximal longitudinal reinforcement. or s and or' s , width of rust-induced cracks in distal and proximal longitudinal reinforcement w and w′ Initial reinforcement area of ​​distal and proximal longitudinal bars A s0 and A' s0 Initial diameter of distal and proximal longitudinal reinforcement d 0 and d' 0; Average corrosion rate of distal and proximal stirrups or v and or' v Width of rust-induced cracks in the distal and proximal stirrups w v and w' v Initial diameter of stirrups d v0 ; Elastic modulus of the uncorroded distal longitudinal reinforcement E s0 Yield strength f y0 Ultimate strength f u0 Yield strain e y0 Strengthening Response e sh0 Ultimate strain e u0 ; Elastic modulus of uncorroded near-side reinforcing bars E' s0 Yield strength f' y0 Yield strain e' y0 Maximum spacing between adjacent unrusted broken stirrupss ; Cross-sectional width after corrosion damage b c Height of cross section after corrosion damage h c Effective height of the cross-section after corrosion damage h 0c Distance from the edge of the cross section after corrosion damage on the distal and proximal sides to the resultant point of the longitudinal reinforcement on that side. a sc and a′ sc ; Reduction coefficient for cross-sectional damage caused by corrosion of distal and proximal reinforcing bars f and f′ ; Reduction coefficient for cross-sectional damage caused by corrosion of distal and proximal longitudinal reinforcement f s and f′ s ; Reduction coefficient for cross-sectional damage caused by corrosion of distal and proximal stirrups f v and f′ v The critical corrosion rate for corrosion of the distal and proximal longitudinal reinforcement leading to rust expansion and spalling of the concrete cover. or s,sp and or' s,sp The critical corrosion rate for rust expansion and spalling of the concrete cover due to corrosion of the distal and proximal stirrups. or v,sp , or' v,sp Actual ultimate stress of the proximal longitudinal reinforcement f′ bc and the strain when the near-side longitudinal reinforcement reaches the actual ultimate stress e' bc ; Critical axial force arm for zero stress in distal longitudinal reinforcement e tc The distance from the point of application of the axial force to the resultant point of the distal longitudinal reinforcement. e The proximal longitudinal reinforcement is just at the critical height of the compression zone for yielding / buckling. ξ′ bb .

[0010] Step 2) Calculate the limit corrosion rate of the corroded eccentrically compressed concrete member and determine the eccentrically compressed failure mode;

[0011] The aforementioned limit corrosion rate and eccentric compression failure mode are determined by the critical axial force arm of the distal longitudinal reinforcement at zero stress. e tc Distance from the point of application of the axial force to the resultant point of the distal longitudinal reinforcement e The size relationships are divided into two categories:

[0012] Limit corrosion rate includes limit I c Corrosion rate orsbb ( e < e tc Boundary I t Corrosion rate or syb Boundary II t Corrosion rate or shb Boundary III t Corrosion rate or sub ( e ≥ e tc );

[0013] Eccentric compression failure modes include mode ① c (0≤) or s < or sbb ), Mode ② c ( or sbb ≤ or s ≤1)( e < e tc ); Mode ① t (0≤) or s < or syb ), Mode ② t ( or syb ≤ or s < or shb ), Pattern ③ t ( or shb ≤ or s < or sub ), Pattern 4 t ( or sub ≤ or s ≤1)( e ≥ e tc );

[0014] Step 3) Calculate the eccentric compressive bearing capacity of the corroded reinforced concrete member corresponding to different failure modes;

[0015] The eccentric compressive bearing capacity of the corroded reinforced concrete member includes mode ① c Mode ② c Pattern ①t Mode ② t Pattern ③ t Pattern 4 t The corresponding eccentric compressive bearing capacity of corroded reinforced concrete members.

[0016] Step 2)

[0017] Boundary I c It is defined as follows: When a corroded reinforced concrete member fails under the action of eccentric axial force, the concrete near the edge is crushed and the longitudinal reinforcement on the far side is just under compressive yielding / buckling.

[0018] Boundary I t It is defined as follows: when a corroded reinforced concrete member fails under the action of eccentric axial force, the concrete near the edge is crushed and the longitudinal reinforcement on the far side just yields under tension.

[0019] Boundary II t It is defined as follows: when a corroded reinforced concrete member fails under the action of eccentric axial force, the concrete near the edge is crushed and the longitudinal reinforcement on the far side is just tensile-strengthened.

[0020] Boundary III t The definition is: when a corroded reinforced concrete member fails under eccentric axial force, the concrete near the edge is crushed and the longitudinal reinforcement on the far side just breaks under tension.

[0021] Step 2)

[0022] Mode ① c It is defined as follows: When a corroded reinforced concrete member fails under the action of eccentric axial force, the concrete near the edge is crushed, while the longitudinal reinforcement on the far side remains in a state of compressive elasticity.

[0023] Mode ② c It is defined as follows: When a corroded reinforced concrete member fails under the action of eccentric axial force, the concrete near the edge is crushed and the longitudinal reinforcement on the far side is in a state of compressive yielding / buckling.

[0024] Mode ① t It is defined as follows: When a corroded reinforced concrete member fails under the action of eccentric axial force, the concrete near the edge is crushed, while the longitudinal reinforcement on the far side remains in a state of tensile elasticity.

[0025] Mode ② t It is defined as follows: When a corroded reinforced concrete member fails under the action of eccentric axial force, the concrete near the edge is crushed and the longitudinal reinforcement on the far side is in a state of tensile yielding.

[0026] Pattern ③ tIt is defined as follows: When a corroded reinforced concrete member fails under the action of eccentric axial force, the concrete near the edge is crushed and the longitudinal reinforcement on the far side is in a state of tensile strengthening.

[0027] Mode 4 t Defined as follows: When a corroded reinforced concrete member fails under eccentric axial force, the concrete near the edge is crushed, and the longitudinal reinforcement on the far side is in a state of tensile fracture.

[0028] The boundary I c Corrosion rate or sbb The method for determining it includes the following steps:

[0029] Step 211) Let in sc = f′ bc , s sc = f bc ( or s ), x = β 1 h c , in sc and s sc These represent the stresses of the longitudinal reinforcement bars in the near and far sides, respectively, due to corrosion. f′ bc and f bc These represent the ultimate compressive stresses of the longitudinal reinforcement bars with corrosion on the near and far sides, respectively. x The height of the pressure zone. β 1 represents the correlation coefficient of the equivalent rectangular stress diagram; where, f′ bc and f bc Each by f′ bcc , f′ yc and f bcc , f yc The smaller value in is determined. f′ bcc and f bcc These are the calculated buckling stress values ​​for the longitudinal reinforcement bars with corrosion on the near and far sides, respectively. f′ yc and f yc Let be the yield stresses of the near-side and far-side rusted longitudinal reinforcements, respectively; substituting these values ​​into the force and moment equilibrium equations, we can obtain the following... ors one dollar at a time ( f bc = f yc ( or s )) or quadratic ( f bc = f bcc ( or s ))equation;

[0030] Step 212) Solve for bounds I c Corrosion rate or sbb ;

[0031] Step 2121) Solve the above problem regarding... or s one dollar at a time ( f bc = f yc ( or s Equation, take or s The solutions in the range (0~0.8) are considered as boundary I. c Undetermined solution for corrosion rate or s1 * ;like or s There is no solution within this range, indicating that for corroded reinforced concrete members with this initial reinforcement information and cross-sectional dimensions, there is no boundary I. c At this time, if or s The calculated value is less than 0, so take... or s1 * =0; if or s The calculated value is greater than 0.8, so take... or s1 * =0.8; or s1 * Substitution f yc ( or s The bounding function can be obtained from the expression. c Yield stress value of lower distal longitudinal reinforcement f yc * ( or s1 * );

[0032] Step 2122) Solve the above problem regarding... or s One-dimensional quadratic ( f bc = f bcc ( or s Equation, take or s The solutions in the range (0~0.8) are considered as boundary I. c Undetermined solution for corrosion rate or s2 * ;like or s There is no solution within this range, indicating that for corroded reinforced concrete members with this initial reinforcement information and cross-sectional dimensions, there is no boundary I. c If the equation has a solution and the solution is less than 0, take... or s2 * =0; if the solution is greater than 0.8, take or s2 * =0.8; if the equation has no solution, take or s2 * =0.8; or s2 * Substitution f bcc ( or s Boundary I can then be obtained. c Ultimate compressive stress value of the lower distal longitudinal reinforcement f bcc * ( or s2 * );

[0033] Step 2123) Comparison f yc * ( or s1 * ), f bcc * ( or s2 * Size Determination Boundaries I c Corrosion rate or sbb ,like f yc * ( ors1 * )< f bcc * ( or s2 * ), take boundary I c Corrosion rate or sbb = or s1 * ;like f yc * ( or s1 * )≥ f bcc * ( or s2 * ), take boundary I c Corrosion rate or sbb = or s2 * .

[0034] The boundary I t Corrosion rate or syb The method for determining it includes the following steps:

[0035] Step 221) Let e sc = e yc ( or s ), s sc = f yc ( or s ), e ct = e cu In the formula, e sc For the strain of the longitudinal reinforcement due to corrosion on the distal side, e yc For the yield strain of the longitudinal reinforcement with corrosion on the distal side, e ct This represents the compressive strain at the near-side concrete edge. e cu The ultimate compressive strain of the concrete is given, and it is assumed that the near-side corroded longitudinal reinforcement has already yielded / buckled under compression. in sc = f′ bcSubstitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x Linear approximation x Given the relative height of the pressure zone, we can obtain information about... or s The linear equation of one variable (0≤ or s ≤0.3) or a quadratic equation (0.3 < or s ≤0.8);

[0036] Step 222) Solve for bounds I t Corrosion rate or syb ;

[0037] Step 2221) Solve the equation and take... or s The smaller solution within the corresponding range is taken as boundary I. t Corrosion rate undetermined solution or syb * ;like or s The calculated value is less than 0, so take... or syb * =0; if or s The calculated value is greater than 0.8, so take... or syb * =0.8; or syb * Substitution e yc ( or s ),make e sc = e yc , e ct = e cu Substituting these values ​​into the deformation compatibility equation yields the undetermined value of the relative compression zone height. x yb * ;

[0038] Step 2222) Comparison x yb * The height of the compression zone relative to the critical compressive yield / buckling point of the proximal longitudinal reinforcement. ξ′ bbThe size assessment assumes that the proximal corroded longitudinal reinforcement has been compressively yielded / buckled. If... x yb * ≥ ξ′ bb The assumption that the near-side corroded longitudinal reinforcement has undergone compressive yielding / buckling holds true, boundary I. t Corrosion rate or syb = or syb * relative pressure zone height x yb = x yb * ;like x yb * < ξ′ bb If the longitudinal reinforcement near the corrosion point is compressed but does not yield / buckle, in sc = E′ sc e' sc , E′ sc , e' sc The elastic modulus and strain of the near-side corroded longitudinal reinforcement are respectively substituted into the force and moment equilibrium equation. x (1- x / 2) Items about x A linear approximation, re-establishing the force and moment equilibrium equations, and simplification yields the following: or s The linear equation of one variable (0≤ or s ≤0.3) or a quadratic equation (0.3 < or s ≤0.8), solve or syb and x yb ;Pick or s The smaller solution within the corresponding range is taken as boundary I. t Corrosion rate or syb ;like or s The calculated value is less than 0, so take... or syb =0; if or s The calculated value is greater than 0.8, so take... or syb =0.8; orsyb Substitution e yc ( or s ),make e sc = e yc , e ct = e cu Substituting these values ​​into the deformation compatibility equation yields the relative height of the compression zone. x yb .

[0039] The boundary II t Corrosion rate or shb The method for determining it includes the following steps:

[0040] Step 231) Let e sc = e shc ( or s ), s sc = f yc ( or s (Only consider 0≤) or s ≤0.3) e ct = e cu In the formula, e shc The strain is used to strengthen the longitudinal reinforcement of the distal corrosion rib, and it is assumed that the proximal corrosion rib has already yielded / buckled under compression. in sc = f′ bc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation yields information about or s The quadratic equation of

[0041] Step 232) Solve for Boundary II t Corrosion rate or shb ;

[0042] Step 2321) Solve the equation and take... or s exist( or syb ~ or s,cr The smaller solution within the range is used as boundary II. t Corrosion rate undetermined solution or shb * , or s,cr The critical corrosion rate at which the yield plateau of the corroded steel bar disappears is given. For accelerated corrosion conditions, the corrosion rates of deformed steel bars and plain round steel bars are... or s,cr These can be taken as 0.3 and 0.15 respectively; for natural corrosion, the values ​​for deformed steel bars and plain round steel bars are... or s,cr It can be taken as 0.2 and 0.1 respectively; if or s There is no solution within this range, indicating that for corroded reinforced concrete members with this initial reinforcement information and cross-sectional dimensions, there is no boundary II. t ,Pick or shb * = or syb ;Will or shb * Substitution e shc ( or s ),make e sc = e shc , e ct = e cu Substituting the values ​​into the deformation compatibility equation yields the undetermined value of the relative compression zone height. x hb * ;

[0043] Step 2322) Comparison x hb * and ξ′ bb The size assessment assumes that the proximal corroded longitudinal reinforcement has been compressively yielded / buckled. If... x hb * ≥ ξ′ bb This indicates that the assumption that the proximal corroded longitudinal reinforcement has been compressively yielded / buckled is correct, and the boundary II is correct. t Corrosion rate or shb = or shb * relative pressure zone height xhb = x hb * ;like x hb * < ξ′ bb If the longitudinal reinforcement near the corrosion point is compressed but does not yield / buckle, in sc = E′ sc e' sc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation, re-establishing the force and moment equilibrium equations, and simplification yields the following: or s Solve the quadratic equation in one variable. or shb and x hb ;Pick or s exist( or syb ~ or s,cr The smaller solution within the range is used as boundary II. t Corrosion rate or shb ;like or s There is no solution within this range, indicating that for corroded reinforced concrete members with this initial reinforcement information and cross-sectional dimensions, there is no boundary II. t ,Pick or shb = or syb ;Will or shb Substitution e shc ( or s ),make e sc = e shc , e ct = e cu Substituting these values ​​into the deformation compatibility equation yields the relative height of the compression zone. x hb .

[0044] The boundary III t Corrosion rate or sub The method for determining it includes the following steps:

[0045] Step 241) Let e sc = e suc ( or s ), s sc = f uc ( or s ), e ct = e cu , f uc , e suc The ultimate stress and ultimate strain of the distal corroded longitudinal reinforcement are given, respectively, and it is assumed that the proximal corroded longitudinal reinforcement has already undergone compressive yielding / buckling. in sc = f′ bc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation yields information about or s The quadratic equation of

[0046] Step 242) Solve for boundary III t Corrosion rate or sub ;

[0047] Step 2421) Solve the equation and take... or s exist( or shb The smaller solution within the range of ~0.8) is taken as boundary III. t Corrosion rate undetermined solution or sub * ;like or s There is no solution within this range, indicating that for corroded reinforced concrete members with this initial reinforcement information and cross-sectional dimensions, there is no boundary III. t ,Pick or sub * =0.8; or sub * Substitution e suc ( or s ),make esc = e suc , e ct = e cu Substituting these values ​​into the deformation compatibility equation yields the undetermined value of the relative compression zone height. x ub * ;

[0048] Step 2422) If x ub * ≥ ξ′ bb This confirms the assumption that the proximal corroded longitudinal reinforcement has been correctly compressively yielded / buckled, and the boundary is III. t Corrosion rate or sub = or sub * relative pressure zone height x ub = x ub * ;like x ub * < ξ′ bb If the longitudinal reinforcement near the corrosion point is compressed but does not yield / buckle, in sc = E′ sc e' sc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x Linear approximation, re-establish and solve the force and moment equilibrium equations. or sub and x ub , can obtain information about or s The quadratic equation of , take or s exist( or shb The smaller solution within the range of ~0.8) is taken as boundary III. t Corrosion rate or sub ;like or s There is no solution within this range, indicating that for corroded reinforced concrete members with this initial reinforcement information and cross-sectional dimensions, there is no boundary III. t ,Pick orsub =0.8; or sub Substitution e suc ( or s ),make e sc = e suc , e ct = e cu Substituting these values ​​into the deformation compatibility equation yields the relative height of the compression zone. x ub .

[0049] Step 3) includes the following steps:

[0050] Step 31) Determine the pattern ① c (0≤) or s < or sbb The calculation steps for the eccentric compressive bearing capacity of the corresponding corroded reinforced concrete member are as follows:

[0051] Take the height of the compression zone of the cross section x = β 1 h c The proximal longitudinal reinforcement can generally be subjected to compressive yielding / buckling. in sc = f′ bc Substituting into the moment equilibrium equation, we can easily obtain mode ①. c Eccentric compression bearing capacity N cu .

[0052] Step 32) Determine Pattern ② c ( or sbb ≤ or s The calculation steps for the eccentric compressive bearing capacity of the corroded reinforced concrete member corresponding to ≤1) are as follows:

[0053] Pick x = β 1 h c , in sc = f′ bc , s sc = f bc (Considering that when 0.8≤ or sWhen the value is ≤1.0, the corrosion degree of the longitudinal reinforcement is too high, and a safer approach is to take ≤1.0. f bc =0), substituting into the force equilibrium equation, mode ② can be directly obtained. c Eccentric compression bearing capacity N cu .

[0054] Step 33) Determine the pattern ① t (0≤) or s < or syb The calculation steps for the eccentric compressive bearing capacity of the corresponding corroded reinforced concrete member are as follows:

[0055] Step 331) Take s sc = E sc e sc , E sc For the elastic modulus of the distal rusted longitudinal reinforcement, let e ct = e cu Substituting into the deformation compatibility equation, we can obtain e sc = e cu ( β 1 / x –1), then s sc = E sc e cu ( β 1 / x –1), and assume that the proximal longitudinal reinforcement has been compressively yielded / buckled. in sc = f′ bc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation yields information about x The quadratic equation of

[0056] Step 332) Solve the equation and take... x exist( x yb , β 1) The larger solution within the range is taken as the undetermined solution for the relative height of the pressure zone. x * ;like x *≥ ξ′ bb This indicates that the assumption that the proximal corroded longitudinal reinforcement has been correctly compressively yielded / buckled is correct. x = x * ,Will s sc = E sc e sc , in sc = f′ bc and x Substituting into the force equilibrium equation, we can obtain mode ① t Eccentric compression bearing capacity N cu ;like x * < ξ′ bb If the assumption is incorrect, let in sc = E′ sc e' sc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation yields information about x A quadratic equation in one variable; solve the equation, taking... x exist( x yb , β 1) The larger solution within the range is taken as the relative height of the pressure zone. x ,Will s sc = E sc e sc , in sc = E′ sc e' sc and x Substituting into the force equilibrium equation, we can obtain mode ① t Eccentric compression bearing capacity N cu .

[0057] Step 34) Determine Pattern ② t ( or syb ≤ or s < or shbThe calculation steps for the eccentric compressive bearing capacity of the corresponding corroded reinforced concrete member are as follows:

[0058] Step 341) Take s sc = f yc And assume in sc = f′ bc Substituting into the force and moment equilibrium equations, we can obtain the following about x The quadratic equation of

[0059] Step 342) Solve the equation and take... x exist( x hb , x yb The larger solution within the range is taken as the undetermined solution for the relative pressure zone height. x * ;like x * ≥ ξ′ bb This indicates that the assumption that the proximal corroded longitudinal reinforcement has been compressively yielded / buckled is valid. x = x * ,Will s sc = f yc , in sc = f′ bc and x Substituting into the force equilibrium equation, we can obtain mode ② t Eccentric compression bearing capacity N cu ;like x * < ξ′ bb If the assumption is false, then the assumption is not true; let in sc = E′ sc e' sc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation yields information about x A quadratic equation in one variable: Solve the equation, take... x exist( x hb , x yb The larger solution within the range is taken as the relative height of the pressure zone. x ,Will s sc = f yc , in sc = E′ sc e' sc and x Substituting into the force equilibrium equation, we can obtain mode ② t Eccentric compression bearing capacity N cu .

[0060] Step 35) Determine Pattern ③ t ( or shb ≤ or s < or sub The calculation steps for the eccentric compressive bearing capacity of the corresponding corroded reinforced concrete member are as follows:

[0061] Step 351) Take s sc = f yc + E shc ( e sc - e shc ), E shc To strengthen the modulus of the longitudinal reinforcement for distal corrosion, e ct = e cu Substituting into the deformation compatibility equation, we can obtain e sc = e cu ( β 1 / x –1), then s sc = f yc + E shc [ e cu ( β 1 / x –1)– e shc [And assume that the proximal longitudinal reinforcement has been compressed and yielded / buckled,] in sc = f′ bc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation yields information about x The quadratic equation of

[0062] Step 352) Solve the equation and take... x exist( x ub , x hb The larger solution within the range is taken as the undetermined solution for the relative pressure zone height. x * ;like x * ≥ ξ′ bb Then it is assumed that the near-side corroded longitudinal reinforcement has been compressively yielded / buckled; let x = x * ,Will s sc = f yc + E shc [ e cu ( β 1 / x –1)– e shc ]、 in sc = f′ bc and x Substituting into the force equilibrium equation, we can obtain mode ③. t Eccentric compression bearing capacity N cu ;like x * < ξ′ bb If , then the assumption is false. Let in sc = E′ sc e' sc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation yields information about x A quadratic equation in one variable; solve the equation, taking... x exist( x ub , x hb The larger solution within the range is taken as the relative height of the pressure zone. x ,Will ssc = f yc + E shc [ e cu ( β 1 / x –1)– e shc ]、 in sc = E′ sc e' sc and x Substituting into the force equilibrium equation, we can obtain mode ③. t Eccentric compression bearing capacity N cu .

[0063] Step 36) Determine Pattern ④ t ( or sub ≤ or s The calculation steps for the eccentric compressive bearing capacity of the corroded reinforced concrete member corresponding to ≤1) are as follows:

[0064] Step 361) Calculate the flexural capacity by using the ultimate compressive stress of the near longitudinal reinforcement or the ultimate tensile stress of the far longitudinal reinforcement. M u1 The calculation formula is:

[0065]

[0066] Step 362) Calculate the width as b c Height is h 0c Cracking moment of plain concrete beam M u2 The calculation formula is:

[0067]

[0068] Step 363) by M u1 and M u2 Larger value determination pattern ④ t Bending capacity of eccentrically compressed members M u The calculation formula is:

[0069]

[0070] Step 364) will Mu Dividing by the distance between the axial force and the centerline of the section height after rusting, we can obtain pattern ④. t Eccentric compression bearing capacity N cu The calculation formula is:

[0071]

[0072] In the formula e 0 represents the distance from the axial pressure to the center point of the initial cross-section; e cor Add an eccentricity to prevent corrosion.

[0073] Step 1) Initial (uncorroded) cross-sectional width b Initial cross-section height h Initial cross-section effective height h 0. Thickness of the concrete protective layer on the far and near sides c and c' Distance from the edge of the initial section on the far and near sides to the resultant point of the longitudinal reinforcement on that side a s and a′ s Concrete strength grade, concrete compressive strength f c Concrete tensile strength f t The types of deformed or plain longitudinal reinforcement and stirrups, and the average corrosion rate of distal and proximal longitudinal reinforcement. or s and or' s Width of rust-induced cracks in distal and proximal longitudinal reinforcement w and w′ Initial reinforcement area of ​​distal and proximal longitudinal bars A s0 and A' s0 Initial diameter of distal and proximal longitudinal reinforcement d 0 and d' 0. Average corrosion rate of distal and proximal stirrups or v and or' v Width of rust-induced cracks in the distal and proximal stirrups w v and w' v Initial diameter of stirrups d v0 Elastic modulus of the uncorroded distal longitudinal reinforcement E s0 Yield strength f y0 Ultimate strengthf u0 Yield strain e y0 Strengthening Response e sh0 Ultimate strain e u0 Elastic modulus of uncorroded near-side reinforcing bars E' s0 Yield strength f' y0 Yield strain e' y0 Maximum spacing between adjacent unrusted broken stirrups s The parameters can be measured according to the method described in GB / T 50784-2013 "Technical Standard for On-site Testing of Concrete Structures"; if the mechanical performance parameters of uncorroded steel bars are inconvenient to obtain, the values ​​can be obtained by referring to the table of common initial mechanical performance parameters of steel bars, as shown in Table 1.

[0074] Table 1 Initial Measured Mechanical Properties of Commonly Used Steel Reinforcing Bars

[0075]

[0076] Step 1)

[0077] 1) Width of cross-section after corrosion damage b c The calculation method is as follows:

[0078] If actual observation shows that corrosion of the stirrups along the height direction has led to the spalling of the concrete cover, then the cross-sectional width after corrosion damage can be taken as... b c = b - c b - c′ b ,in, b The initial cross-sectional width, c b , c′ b These represent the initial concrete cover thicknesses for the stirrups on both sides of the width direction; if no spalling of the stirrup cover is observed along the height direction, then it can be approximated as... b c = b That is, the weakening effect of stirrup corrosion on the width direction of the cross section is not considered.

[0079] 2) Height of the cross-section after corrosion damage h c The calculation method is as follows:

[0080]

[0081] 3) Effective height of the cross-section after corrosion damage h 0c The calculation method is as follows:

[0082]

[0083] 4) Distance from the edge of the cross-section after corrosion damage on the distal and proximal sides to the resultant point of the longitudinal reinforcement on that side. a sc and a′ sc The calculation method is as follows:

[0084]

[0085] 5) Reduction coefficient for cross-sectional damage caused by corrosion of distal and proximal reinforcing bars f and f′ The calculation method is as follows:

[0086]

[0087] 6) Reduction coefficient for section damage caused by corrosion of distal and proximal longitudinal reinforcement f s and f′ s The calculation method is as follows:

[0088]

[0089] In the formula, w cr , w′ cr These represent the critical rust-expansion crack widths caused by corrosion of the far and near longitudinal reinforcements leading to spalling of the concrete cover; for deformed reinforcements, take... w cr , w′ cr For plain round steel bars, take 3.5 mm; w cr , w′ cr It is 2.5 mm.

[0090] 7) Reduction coefficient for section damage caused by corrosion of distal and proximal stirrups f v and f′ v The calculation method is as follows:

[0091]

[0092] In the formula, w vcr , w′ vcrThese represent the critical rust-expansion crack widths caused by the corrosion of the far and near stirrups leading to the spalling of the concrete cover; for deformed reinforcing bars, take... w vcr , w′ vcr For plain round steel bars, take 3.5 mm; w vcr , w′ vcr It is 2.5 mm.

[0093] 8) Critical corrosion rate for rust expansion and spalling of concrete cover caused by corrosion of distal and proximal longitudinal reinforcement or s,sp and or' s,sp The calculation method is as follows:

[0094]

[0095] 9) Critical corrosion rate for rust expansion and spalling of concrete cover caused by corrosion of distal and proximal stirrups or v,sp , or' v,sp The calculation method is as follows:

[0096]

[0097] 10) Actual ultimate stress of the proximal longitudinal reinforcement f′ bc The calculation method is as follows:

[0098]

[0099]

[0100]

[0101] E' sc = E' s0

[0102] In the formula, f′ yc The yield stress of the longitudinal reinforcement with near-side corrosion; f′ bbc This is the calculated value of the buckling stress of the longitudinal reinforcement near the corrosion site; E' sc The elastic modulus of the near-side corroded steel bar; µ For the effective length coefficient, take µ =1.0.

[0103] 11) Strain when the proximal longitudinal reinforcement reaches the actual ultimate stress e' bc The calculation method is as follows:

[0104]

[0105] 12) Critical axial force lever arm for zero stress of distal longitudinal reinforcement e tc The calculation method is as follows:

[0106]

[0107] 13) Distance from the point of application of the axial force to the resultant point of the distal longitudinal reinforcement e The calculation method is as follows:

[0108]

[0109] In the formula, or nsc Consideration for reinforced concrete columns after corrosion damage P - ∆ The moment amplification factor of the effect; e i This is the actual initial eccentricity; or nsc , e i The values ​​or calculations can be obtained by referring to the "Code for Design of Concrete Structures (GB50010-2010)".

[0110] 14) The height of the relative compression zone at the critical point of yielding / buckling of the proximal longitudinal reinforcement. ξ′ bb The calculation method is as follows:

[0111]

[0112] In the formula, e' bc To ensure that the proximal longitudinal reinforcement reaches the actual ultimate stress f′ bc Response in time.

[0113] Step 2)

[0114] 1) The force balance equation is:

[0115]

[0116] 2) The moment equilibrium equation is:

[0117]

[0118] 3) The deformation compatibility equation is:

[0119]

[0120] 4) In the moment equilibrium equation x (1- x / 2) Items about x The linear approximation is calculated using the following formula:

[0121]

[0122] 5) The formula for calculating the yield stress of corroded tensile steel bars is:

[0123]

[0124] 6) Calculation of buckling stress of the distal corrosion longitudinal reinforcement, the calculation formula is:

[0125]

[0126] 7) The ultimate compressive stress of the longitudinal reinforcement with distal corrosion is calculated using the following formula:

[0127]

[0128] 8) The ultimate stress of the longitudinal reinforcement with corrosion on the far side is calculated using the following formula:

[0129]

[0130] 9) The yield strain of the longitudinal reinforcement with distal corrosion is calculated using the following formula:

[0131]

[0132] 10) The formula for calculating the strengthening strain of the longitudinal reinforcement in the distal corrosion zone is:

[0133]

[0134] 11) The ultimate strain of the longitudinal reinforcement with distal corrosion is calculated using the following formula:

[0135]

[0136] Step 3)

[0137] 1) The elastic modulus of the longitudinal ribs with distal corrosion is calculated using the following formula:

[0138] E sc = E s0

[0139] 2) The modulus of reinforcement of the longitudinal ribs with distal corrosion is calculated using the following formula:

[0140]

[0141] 3) The additional eccentricity due to corrosion is calculated using the following formula:

[0142] e cor =( a ′ s f ′- a s f ) / 2

[0143] Compared with the prior art, the present invention has the following beneficial effects:

[0144] This invention, by considering the degradation of the mechanical properties of reinforcing bars due to corrosion, and through cross-sectional analysis, determines the critical axial force arm of the distal longitudinal reinforcement at zero stress. e tc Distance from the point of application of the axial force to the resultant point of the distal longitudinal reinforcement e By analyzing the magnitude of the corrosion rate, one or three threshold corrosion rates can be accurately calculated. Based on this, two or four failure modes can be distinguished. When a reinforced concrete member under eccentric compression fails, the actual stress state of the steel bars on the side away from the axial force and the side close to the axial force can be determined. This allows for the determination of the failure mode of the reinforced concrete member under eccentric compression with a known corrosion rate. Based on this, the eccentric compressive bearing capacity of the reinforced concrete member under the corresponding failure mode can be analyzed. This method has the advantages of clear concept, simple calculation, and strong practicality. Attached Figure Description

[0145] Figure 1 This is a flowchart of the method of the present invention.

[0146] Figure 2 The stress and strain distribution diagrams of the eccentrically compressed corroded reinforced concrete member of the present invention are shown in the figure. (2a) is the stress distribution diagram, (2b) is the strain distribution diagram, and (2c) is the equivalent stress distribution diagram. Detailed Implementation

[0147] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0148] In this embodiment, 18 eccentrically compressed and corroded reinforced concrete members with different degrees of corrosion were obtained in a laboratory in Shanghai using an electric current-accelerated corrosion method. The bearing capacity of the normal section of these 18 eccentrically compressed and corroded reinforced concrete members was calculated to verify the method described in this invention.

[0149] This embodiment provides a method for analyzing the eccentric compressive bearing capacity of corroded reinforced concrete columns, such as... Figure 1 As shown, it includes the following steps:

[0150] Step 1) Measure and calculate the basic parameters of the eccentrically compressed reinforced concrete member before and after corrosion.

[0151] According to the method described in GB / T 50784-2013 "Technical Standard for On-site Testing of Concrete Structures", the 18 eccentrically loaded and corroded reinforced concrete members with different degrees of corrosion were all found to have rectangular cross-sections, with the initial (uncorroded) cross-sectional width... b The initial cross-sectional height is 200mm. h The effective height of the initial section is 200 mm. h 0 is 153 mm, the thickness of the concrete protective layer on the distal and proximal sides. c and c' Both are 30 mm, representing the distance from the edge of the initial section on the far and near sides to the resultant point of the longitudinal reinforcement on that side. a s and a′ s All are 47 mm thick. The concrete strength grade is less than C50, and the concrete compressive strength is... f c The concrete tensile strength is 28.33 MPa. f t The strength is 2.8 MPa. Both the proximal and distal longitudinal reinforcements are configured with 2... 18mm steel bars, stirrup configuration 8@100, from which the initial reinforcement area of ​​the distal and proximal longitudinal bars can be determined. A s0 = A' s0 =508.938 mm 2 Initial diameter of distal and proximal longitudinal reinforcement d 0= d' 0=18 mm, initial diameter of stirrups d v0 =8 mm. The elastic modulus of the uncorroded distal longitudinal reinforcement was measured. E s0 =2.047×10 5 MPa, yield strength f y0 =376.27 MPa, ultimate strength f u0 =550.259 MPa, yield strain e y0 =0.001838, Enhanced strain e sh0 =0.023, ultimate strain e u0 =0.143, elastic modulus of the uncorroded near-side reinforcing steel. E' s0 =2.047×105 MPa, yield strength f' y0 =376.27 MPa, yield strain e' y0 =0.001838. The average corrosion rate of the distal and proximal longitudinal reinforcements was measured. or s and or' s Average corrosion rate of distal and proximal stirrups or v and or' v As shown in Table 1. Due to the rust expansion crack width of the distal and proximal longitudinal reinforcement. w and w′ Width of rust-induced cracks in the distal and proximal stirrups w v and w' v Not specified, calculated by default as 0 mm. Maximum spacing between adjacent unrusted broken stirrups. s All are 100 mm. Actual initial eccentricity. e i and normal section bearing capacity N cu,exp As shown in Table 2.

[0152] Table 2. Degree of Reinforcing Steel Corrosion and Test Information

[0153]

[0154] Based on the above-mentioned formulas, the cross-sectional width after corrosion damage can be calculated. b c Height of cross section after corrosion damage h c Effective height of the cross-section after corrosion damage h 0c Distance from the edge of the cross section after corrosion damage on the distal and proximal sides to the resultant point of the longitudinal reinforcement on that side. a sc and a′ sc (Reduction factor for cross-sectional damage caused by corrosion of distant and near steel bars) f and f′ Reduction coefficient for cross-sectional damage caused by corrosion of distal and proximal longitudinal reinforcement. f s and f′ s Reduction coefficient for cross-sectional damage caused by corrosion of distal and proximal stirrups f v and f′ v Critical corrosion rate for rust expansion and spalling of concrete cover caused by corrosion of distal and proximal longitudinal reinforcement. or s,sp and or' s,sp Critical corrosion rate for rust expansion and spalling of concrete cover caused by corrosion of distal and proximal stirrups. or v,sp , or' v,sp (Determined) Actual ultimate stress of the proximal longitudinal reinforcement f′ bc and the strain when the near-side longitudinal reinforcement reaches the actual ultimate stress e' bc The critical axial force arm of the distal longitudinal reinforcement at zero stress e tc The distance from the point of application of the axial force to the resultant point of the distal longitudinal reinforcement. e The height of the near longitudinal reinforcement is just at the critical point of compressive yield / buckling relative to the compression zone. ξ′ bb As shown in Table 3.

[0155] Table 3 Basic parameters for calculating eccentrically compressed reinforced concrete members

[0156]

[0157] Step 2) Calculate the limit corrosion rate of the corroded eccentrically compressed concrete member based on the basic parameters and determine the eccentrically compressed failure mode.

[0158] The stress and strain distribution diagram of the eccentrically compressed corroded reinforced concrete member is shown below. Figure 2 As shown in Table 3, the specimens in this embodiment... e All greater than e tc That is, when a corroded reinforced concrete member fails under eccentric axial force, the distal longitudinal reinforcement is under tension. Therefore, it is necessary to solve for the limiting corrosion rate I of each specimen. t ~Ⅲ t .

[0159] Specimen ZXY-700-5:

[0160] Step 21) Solve for bounds I t Corrosion rate or syb :

[0161] make e sc = e yc ( or s ), s sc = f yc ( ors ), e ct = e cu =0.0033, and assume that the near-side corroded longitudinal reinforcement has been compressively yielded / buckled. in sc = f′ bc =376.02 MPa, substitute into the force and moment equilibrium equation, and change the value in the moment equilibrium equation. x (1- x / 2) Items about x Linear approximation x Given the relative height of the pressure zone, we can obtain information about... or s The quadratic equation of

[0162]

[0163] Substitute the data:

[0164]

[0165] Simplify and organize:

[0166] when j 1 = 0.825 k 1=0、 j 2=0、 k When 2=1 (must be 0≤) or s ≤0.3、0≤ x (Solve for ≤0.4), we have

[0167]

[0168] Solving or s =3.2298, discarded;

[0169] when j 1 = 0.825 k 1=0、 j 2 = -0.5 k When 2 = 1.15 (requires 0.3 < or s ≤0.8、0≤ x (Solve for ≤0.4), we have

[0170]

[0171] No solution, discard.

[0172] when j 1 = 0.375 k1 = 0.18 j 2=0、 k When 2=1 (must be 0≤) or s ≤0.3, 0.4< x (Solve for ≤0.8), we have

[0173]

[0174] Solving or s =2.6984, discarded;

[0175] when j 1 = 0.375 k 1 = 0.18 j 2 = -0.5 k When 2 = 1.15 (requires 0.3 < or s ≤0.8, 0.4< x (Solve for ≤0.8), we have

[0176]

[0177] Solving or s =2.6195 or or s =6.0809, temporarily taken or s =0.8.

[0178] Pick or syb * =0.8, will or syb * Substitution e yc ( or s ),make e sc = e yc , e ct = e cu Substituting these values ​​into the deformation compatibility equation yields the undetermined value of the relative compression zone height. x yb * :

[0179]

[0180] Assuming the proximal longitudinal reinforcement is under compressive yielding / buckling, therefore boundary I... t Corrosion rate orsyb =0.8, relative height of the pressure zone x yb =0.5917.

[0181] Step 22) Solve for Boundary II t Corrosion rate or shb and Boundary III t Corrosion rate or sub :

[0182] Due to boundary I t Corrosion rate or syb =0.8, and or sub ≥ or shb ≥ or syb ,but or sub = or shb = or syb =0.8.

[0183] Step 23) Determine the eccentric compression failure mode:

[0184] Specimen ZXY-700-5 or s =0 < or syb =0.8, therefore the failure mode of specimen ZXY-700-5 is mode ①. t .

[0185] Step 3) Analyze the eccentric compressive bearing capacity of the corroded reinforced concrete members corresponding to different eccentric compressive failure modes.

[0186] The failure mode of specimen ZXY-700-5 is mode ①. t ,Pick s sc = E sc e sc , E sc For the elastic modulus of the distal rusted longitudinal reinforcement, let e ct = e cu Substituting into the deformation compatibility equation, we can obtain e sc = e cu ( β 1 / x –1), then s sc = E sc e cu ( β 1 / x –1), and assume that the proximal longitudinal reinforcement has been compressively yielded / buckled. in sc = f′ bc Substitute into the force and moment equilibrium equation, and then into the moment equilibrium equation... x (1- x / 2) Items about x A linear approximation yields information about x The quadratic equation of :

[0187]

[0188] Substitute the data:

[0189]

[0190] Solve the equation and take x exist( x yb , β 1) The larger solution within the range is taken as the undetermined solution for the relative height of the pressure zone. x * ,again x yb =0.5917>0.4, therefore take j 1 = 0.375 k 1 = 0.18. Simplifying the above equation, we have...

[0191]

[0192] Solving x =0.7137 or x =-1.0013, therefore x * =0.7137≥ ξ′ bb =0.5427.

[0193] Therefore, assuming the proximal corroded longitudinal reinforcement has correctly undergone compressive yielding / buckling, let x = x * =0.7137, s sc = E sc e sc , in sc =f′ bc and x Substituting into the force equilibrium equation, we can obtain mode ① t Eccentric compression bearing capacity N cu :

[0194]

[0195] Test values ​​of bearing capacity of specimen ZXY-700-5 N cu,exp =742kN, calculated value N cu,cal =761.432kN, N cu,cal / N cu,exp =1.026, indicating that the calculation method of the present invention is accurate and reliable.

[0196] The calculation steps for the eccentric compression normal section bearing capacity of the remaining specimens are the same as those for specimen ZXY-700-5. Using the calculation method of this invention, the eccentric compression normal section bearing capacity of each specimen is calculated, as shown in Table 4.

[0197] Table 4 Calculated and experimental values ​​of eccentric compression bearing capacity of specimens

[0198]

[0199] As shown in Table 4, the average ratio of the calculated to the experimental bearing capacity of each specimen is 1.0234, and the correlation coefficient between the calculated and experimental values ​​is 0.9919. This indicates that the simplified analysis method for the bearing capacity of eccentrically compressed corroded reinforced concrete members provided by this invention has high accuracy and strong practicality.

[0200] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

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