CN109190309A - Aged reinforced concrete beam bridge shear-carrying capacity evaluation method - Google Patents

Aged reinforced concrete beam bridge shear-carrying capacity evaluation method Download PDF

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CN109190309A
CN109190309A CN201811248803.3A CN201811248803A CN109190309A CN 109190309 A CN109190309 A CN 109190309A CN 201811248803 A CN201811248803 A CN 201811248803A CN 109190309 A CN109190309 A CN 109190309A
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马亚飞
鲁保勇
张建仁
王磊
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Changsha University of Science and Technology
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Abstract

Aged reinforced concrete beam bridge shear-carrying capacity evaluation method disclosed by the invention, the corrosion initial time of concrete reinforcing steel is obtained based on the second diffusion law of Fick, consider that Corrosion Reinforcement sectional area reduces the reduction with reinforcement yielding intensity, obtains the active force of reinforcing bar at Diagonal crack；The compressive strain of back load position is obtained by plane cross-section assumption；Pressure section stress balance equation is cut according to beam, establishes critical diagonal crack top concrete compression area height calculation formula, by being integrated to depth of compressive zone, non-cracked concrete section horizontal applied force size is obtained, determines its active position by moment conditions；Based on ultimate shear balance theory, pressure section isolation body unit equilibrium relation is cut by beam, proposes the Calculation Methods of Shear Capacity of aged reinforced concrete beam bridge.Prediction technique of the present invention is reasonable, and generalization is strong, can provide technical support for the security evaluation of military service concrete beam bridge.

Description

Aged reinforced concrete beam bridge shear-carrying capacity evaluation method
Technical field
The present invention relates to treatment rates security evaluation field, in particular to a kind of aged reinforced concrete beam bridge shearing resistance carrying Power evaluation method.
Background technique
Corrosion can reduce reinforcing steel area and reinforced steel bar strength, and the expansive force that the increase of corrosion product volume generates will lead to coagulation Soil rust distending is split, and reduces the caking property between reinforcing bar and concrete, structural bearing capacity is caused to be degenerated.It is existing on steel bar corrosion influence Research focuses mostly in terms of structure anti-bending strength, and the research in terms of shear behavior is relatively fewer.Due to being in steel by shear-steel muscle The outermost layer of tendons skeleton is easier to corrode；Meanwhile compared with flexual reinforcement, the diameter by shear-steel muscle is relatively small, therefore, Corrosion ratio is relatively high.With the horizontal growth of corrosion, the failure mode of reinforced beam may turn from normal section bending failure For oblique section failure by shear, sheared destruction is brittle break, and consequence is destroyed even more serious than bending resistance.Resistance of Reinforced Concrete Structures Scissor mechanism is complicated, and influence factor is more, there is no pervasive shearing resistance theoretical calculation analysis method at present, and current designs specification is to there is abdomen muscle The calculating of beam shear-carrying capacity still uses the model of half.
In view of the above technical problems, some scholars are moved back by the shear behavior of experimental study CORRODED REINFORCED CONCRETE STRUCTURE Law proposes corresponding calculation method, but mainly for no abdomen muscle or only stirrup corrosion beam.China builds some early stage It is furnished with diagonal bar in rc beam bridge, needs the shear-carrying capacity unified calculation method for carrying out aged reinforced concrete beam bridge, And then propose the safety evaluation method of such bridge.
Summary of the invention
The purpose of the present invention is to provide a kind of aged reinforced concrete beam bridge shear-carrying capacity evaluation methods, effectively solve Above-mentioned technical problem.
Effectively to solve above-mentioned technical problem, the technical solution adopted by the present invention is as follows:
Aged reinforced concrete beam bridge shear-carrying capacity evaluation method, method includes the following steps:
(1) it is based on the second diffusion law of Fick, concrete reinforcing steel surface chlorine ion concentration is calculated and reaches criticality chlorine ion The time of concentration determines steel bar corrosion initial time, reduces the reduction with yield strength in conjunction with reinforcing steel area after corrosion, calculates Corrosion Reinforcement intensity；
(2) according to pressure section stress balance equation is cut, by the strain-stress relation of concrete compression, critical oblique segmentation is obtained Top concrete compression area height is stitched, by integrating to depth of compressive zone, obtains non-cracked concrete section horizontal applied force, by Moment conditions determine its active position；
(3) it to pressure section slider progress force analysis is cut, is put down by the upper and lower side concrete slider unit torque of diagonal crack Weigh equation, obtains the shear-carrying capacity calculation formula of aged reinforced concrete beam bridge.
Particularly, the step (1) is further comprising the steps of:
(1-1) be based on the second diffusion law of Fick, by rebar surface chlorine ion concentration reach criticality chlorine ion concentration when Between as corrosion initial time, corrosion initial time indicate are as follows:
In formula, TiFor steel bar corrosion initial time；DcFor diffusion coefficient；C0For concrete surface chlorine ion concentration；Erf is Error function；X is protective layer thickness；CcrFor criticality chlorine ion concentration；
After t, bar diameter D (t) in reinforced beam are as follows:
D (t)=D0-0.0232(t-Ti)icorr(t) (2)
In formula, D0For reinforcing bar initial diameter；icorrIt (t) is corrosion electric current density；
The average cross-section A (t) of Corrosion Reinforcement may be expressed as:
A (t)=π D2(t)/4 (3)
The yield strength of (1-2) Corrosion Reinforcement is directly related with its remaining cross-section product, Corrosion Reinforcement yield strength and corrosion Degree approximation is in a linear relationship, may be expressed as:
In formula, fy0For unattacked reinforcement yielding intensity；fyIt (t) is Corrosion Reinforcement yield strength；αyFor Corrosion Reinforcement intensity Reduction coefficient takes αy=0.9；A0For unattacked reinforcing steel area；
When (1-3) reinforced beam is reached yield strength by shear-steel muscle, the active force of reinforcing bar be may be expressed as: at diagonal crack
Tx=A (t)eff,xf(t)yc,x (5)
Ty=A (t)eff,yf(t)yc,y (6)
Tob=A (t)eff,obf(t)yc,ob (7)
In formula, Tx、TyAnd TobThe pulling force of respectively vertical muscle, stirrup and diagonal bar；f(t)yc,x、f(t)yc,yWith f (t)yc,obRespectively For the yield strength for indulging muscle, stirrup and diagonal bar；A(t)eff,x、A(t)eff,yWith A (t)eff,obRespectively indulge muscle, stirrup and diagonal bar Sectional area.
Particularly, the step (2) is further comprising the steps of:
(2-1) assumes diagonal crack top depth of compressive zone csConcrete compressive strain is ε at arbitrary point in range, and the point is in Distance with axis is x；According to plane cross-section assumption, then csThe horizontal compressive strain ε of range inner concrete are as follows:
In formula, ε0And εcThe respectively corresponding strain (ε of concrete peak stress0=0.002) it and at the top of beams of concrete is pressurized Side strain；h0For the effective cross-section height of beam；x0For the corresponding depth of section of concrete peak stress.ε'xMuscle is indulged for pure bending Strain, is calculated as the following formula:
In formula, EsTo indulge muscle elasticity modulus；M and P is the moment of flexure and shearing for calculating section；α is Diagonal crack and level The inclination angle of vertical muscle.Then back concrete compression side strain indicates are as follows:
Concrete compression strain-stress relation are as follows:
In formula, coefficient n=2- (fcu,k- 50)/60, as n > 2, n=2 is taken；fcu,kFor compressive strength of concrete mark Quasi- value；fcFor concrete axial compressive strength design value；εcuFor the ultimate compressive strain of concrete of normal section；
(2-2) integrates the non-cracked concrete section in diagonal crack top, then compressive region concrete resultant force size are as follows:
In formula, b is deck-siding；
Active force C to diagonal crack top distance are as follows:
Square is taken to critical diagonal crack lower end concrete triangle isolation body unit V T position, is had
In formula, β is the angle of diagonal bar and stirrup；Depth of compressive zone when c is beam pure bending；TfMake to indulge muscle at bending cracks Firmly；
Being rounded a curved scissors region is slider, compressive region concrete point of resultant force C when to pure bendingfSquare is taken, is had:
Tf=Ra/d (15)
In formula, R is end reaction；A is horizontal distance of the load(ing) point to support；D is to indulge muscle to CfPosition it is vertical away from From；
Square is taken to critical diagonal crack upper end triangle isolation body unit active force C point, is had:
In formula, z is distance of the critical diagonal crack top to depth of compressive zone point of resultant force；
It is taken as firmly CfDistance of the point away from beam top edge is 0.4c, then c/h0≈ 0.5, tan α ≈ a/h0, d/h0≈1- 0.4c/h0, it can obtain:
It enablesDiagonal crack top concrete compression area height can be obtained are as follows:
Particularly, the step (3) is further comprising the steps of:
Based on ultimate shear balance theory, closed by beam Diagonal crack upper left side slider unit horizontal direction stress balance System, has:
C-Tx-Tobβ=0 sin (19)
Further, indulging muscle amount of force indicates are as follows:
When shear compression failure occurs for reinforced beam, R=Vu, ultimate shear bearing capacity formula are as follows:
Vu=α1A(t)eff,yf(t)yc,y+α2A(t)eff,obf(t)yc,ob+α3fcbcs (21)
Particularly, this method is further comprising the steps of:
By determining that steel bar corrosion initial time, Corrosion Reinforcement sectional area, Corrosion Reinforcement yield strength, diagonal crack top are oblique Depth of compressive zone csAnd its size and location of range inner concrete horizontal applied force C, then rc beam bridge can be obtained Shear-carrying capacity Vu。
The invention has the benefit that aged reinforced concrete beam bridge shear-carrying capacity evaluation method provided by the invention, Based on limit equilibrium theory, the shear-carrying capacity unified formula of rc beam bridge is established, can effectively consider reinforcing bar Corrosion, component geometric dimension, diagonal bar inclination angle, the strain of compressive region concrete horizontal etc., prediction technique is reasonable, and generalization is strong, can be The shear behavior assessment of military service concrete beam bridge provides technical support.
The present invention is described in detail with reference to the accompanying drawing.
Detailed description of the invention
Fig. 1 is that beam cuts reinforcing bar force diagram at pressure failure and diagonal crack.
Fig. 2 is that body unit calculating schematic diagram is isolated in concrete on the upside of critical diagonal crack.
Fig. 3 is concrete slider cell schematics on the downside of critical diagonal crack.
Stress diagram at critical diagonal crack when Fig. 4 is failure by shear.
Specific embodiment
Embodiment 1:
As shown in Figs 1-4, present embodiment discloses a kind of aged reinforced concrete beam bridge shear-carrying capacity evaluation methods, should Method the following steps are included:
(1) it is based on the second diffusion law of Fick, concrete reinforcing steel surface chlorine ion concentration is calculated and reaches criticality chlorine ion The time of concentration determines steel bar corrosion initial time, reduces the reduction with yield strength in conjunction with reinforcing steel area after corrosion, calculates Corrosion Reinforcement intensity；
(2) according to pressure section stress balance equation is cut, by the strain-stress relation of concrete compression, critical oblique segmentation is obtained Top concrete compression area height is stitched, by integrating to depth of compressive zone, obtains non-cracked concrete section horizontal applied force, by Moment conditions determine its active position；
(3) to pressure section slider progress force analysis is cut, by the upper and lower side slider unit torque balance side of diagonal crack Journey obtains the shear-carrying capacity calculation formula of aged reinforced concrete beam bridge.
The Applicant declares that person of ordinary skill in the field is on the basis of the above embodiments, by above-described embodiment Step is combined with the technical solution of Summary, thus generate new method and record scope of the invention it One, the application is to keep specification concise, no longer enumerates the other embodiment of these steps.
The present embodiment specific implementation is as described below:
The step (1) is further comprising the steps of:
(1-1) be based on the second diffusion law of Fick, by rebar surface chlorine ion concentration reach criticality chlorine ion concentration when Between as corrosion initial time, corrosion initial time indicate are as follows:
In formula, TiFor steel bar corrosion initial time；DcFor diffusion coefficient；C0For concrete surface chlorine ion concentration；Erf is Error function；X is protective layer thickness；CcrFor criticality chlorine ion concentration；
After t, bar diameter D (t) in reinforced beam are as follows:
D (t)=D0-0.0232(t-Ti)icorr(t) (2)
In formula, D0For reinforcing bar initial diameter；icorrIt (t) is corrosion electric current density；
The average cross-section A (t) of Corrosion Reinforcement may be expressed as:
A (t)=π D2(t)/4 (3)
The yield strength of (1-2) Corrosion Reinforcement is directly related with its remaining cross-section product, Corrosion Reinforcement yield strength and corrosion Degree approximation is in a linear relationship, may be expressed as:
In formula, fy0For unattacked reinforcement yielding intensity；fyIt (t) is Corrosion Reinforcement yield strength；αyFor Corrosion Reinforcement intensity Reduction coefficient takes αy=0.9；A0For unattacked reinforcing steel area；
When (1-3) reinforced beam is reached yield strength by shear-steel muscle, the active force of reinforcing bar be may be expressed as: at diagonal crack
Tx=A (t)eff,xf(t)yc,x (5)
Ty=A (t)eff,yf(t)yc,y (6)
Tob=A (t)eff,obf(t)yc,ob (7)
In formula, Tx、TyAnd TobThe pulling force of respectively vertical muscle, stirrup and diagonal bar；f(t)yc,x、f(t)yc,yWith f (t)yc,obRespectively For the yield strength for indulging muscle, stirrup and diagonal bar；A(t)eff,x、A(t)eff,yWith A (t)eff,obRespectively indulge muscle, stirrup and diagonal bar Sectional area.
The step (2) is further comprising the steps of:
(2-1) assumes diagonal crack top depth of compressive zone csConcrete compressive strain is ε at arbitrary point in range, and the point is in Distance with axis is x；According to plane cross-section assumption, then csThe horizontal compressive strain ε of range inner concrete are as follows:
In formula, ε0And εcThe respectively corresponding strain (ε of concrete peak stress0=0.002) it and at the top of beams of concrete is pressurized Side strain；h0For the effective cross-section height of beam；x0For the corresponding depth of section of concrete peak stress.ε'xMuscle is indulged for pure bending Strain, is calculated as the following formula:
In formula, EsTo indulge muscle elasticity modulus；M and P is the moment of flexure and shearing for calculating section；α is Diagonal crack and level The inclination angle of vertical muscle.Then back concrete compression side strain indicates are as follows:
Concrete compression strain-stress relation are as follows:
In formula, coefficient n=2- (fcu,k- 50)/60, as n > 2, n=2 is taken；fcu,kFor compressive strength of concrete mark Quasi- value；fcFor concrete axial compressive strength design value；εcuFor the ultimate compressive strain of concrete of normal section；
(2-2) integrates the non-cracked concrete section in diagonal crack top, then compressive region concrete resultant force size are as follows:
In formula, b is deck-siding；
Active force C to diagonal crack top distance are as follows:
Square is taken to critical diagonal crack lower end concrete triangle isolation body unit V T position, is had
In formula, β is the angle of diagonal bar and stirrup；Depth of compressive zone when c is beam pure bending；TfMake to indulge muscle at bending cracks Firmly；
Being rounded a curved scissors region is slider, to compressive region concrete point of resultant force CfSquare is taken, is had:
Tf=Ra/d (15)
In formula, R is end reaction；A is horizontal distance of the load(ing) point to support；D is to indulge muscle to CfPosition it is vertical away from From；
Square is taken to critical diagonal crack upper end triangle isolation body unit active force C point, is had:
In formula, z is distance of the critical diagonal crack top to depth of compressive zone point of resultant force；
It is taken as firmly CfDistance of the point away from beam top edge is 0.4c, then c/h0≈ 0.5, tan α ≈ a/h0, d/h0≈1- 0.4c/h0, it can obtain:
It enablesDiagonal crack top concrete compression area height can be obtained are as follows:
The step (3) is further comprising the steps of:
Based on ultimate shear balance theory, closed by beam Diagonal crack upper left side slider unit horizontal direction stress balance System, has:
C-Tx-Tobβ=0 sin (19)
Further, indulging muscle amount of force indicates are as follows:
When shear compression failure occurs for reinforced beam, R=Vu, ultimate shear bearing capacity formula are as follows:
Vu=α1A(t)eff,yf(t)yc,y+α2A(t)eff,obf(t)yc,ob+α3fcbcs (21)
By determine steel bar corrosion initial time, Corrosion Reinforcement sectional area, Corrosion Reinforcement yield strength, diagonal crack top by Pressure area height csAnd its size and location of range inner concrete horizontal applied force C, then the anti-of rc beam bridge can be obtained Cut bearing capacity Vu。
The another statement of applicant, implementation method of the invention that the present invention is explained by the above embodiments, but the present invention is simultaneously It is not limited to above embodiment, that is, does not mean that the present invention must rely on the above method and could implement.Technical field Technical staff adds implementation method equivalence replacement and step selected by the present invention it will be clearly understood that any improvement in the present invention Add, the selection of concrete mode etc., all of which fall within the scope of protection and disclosure of the present invention.
In the present embodiment, it is based on limit equilibrium theory, it is unified to establish aged reinforced concrete beam bridge shear-carrying capacity Calculation formula can effectively consider steel bar corrosion, component geometric dimension, diagonal bar inclination angle, the strain of compressive region concrete horizontal etc., prediction Method is reasonable, and generalization is strong, can assess for the shear behavior of military service concrete beam bridge and provide technical support.
Present invention is not limited to the embodiments described above, all using the institute for realizing the object of the invention with similar method of the present invention There is embodiment within that scope of the present invention.

Claims (5)

1. aged reinforced concrete beam bridge shear-carrying capacity evaluation method, which is characterized in that method includes the following steps:
(1) it is based on the second diffusion law of Fick, concrete reinforcing steel surface chlorine ion concentration is calculated and reaches criticality chlorine ion concentration Time, determine steel bar corrosion initial time, in conjunction with after corrosion reinforcing steel area reduce and yield strength reduction, calculate corrosion Reinforced steel bar strength；
(2) according to pressure section stress balance equation is cut, by the strain-stress relation of concrete compression, critical diagonal crack top is obtained Concrete compression area height is held non-cracked concrete section horizontal applied force to be obtained, by torque by integrating to depth of compressive zone Relationship determines its active position；
(3) to pressure section slider progress force analysis is cut, by the upper and lower side concrete slider unit torque balance side of diagonal crack Journey obtains aged reinforced concrete beam bridge shear-carrying capacity calculation formula.
2. aged reinforced concrete beam bridge shear-carrying capacity evaluation method according to claim 1, which is characterized in that the step Suddenly (1) is further comprising the steps of:
(1-1) is based on the second diffusion law of Fick, and the time that rebar surface chlorine ion concentration reaches criticality chlorine ion concentration is made To corrode initial time, corrosion initial time is indicated are as follows:
In formula, TiFor steel bar corrosion initial time；DcFor diffusion coefficient；C0For concrete surface chlorine ion concentration；Erf is error Function；X is protective layer thickness；CcrFor criticality chlorine ion concentration；
After t, bar diameter D (t) in reinforced beam are as follows:
D (t)=D0-0.0232(t-Ti)icorr(t) (2)
In formula, D0For reinforcing bar initial diameter；icorrIt (t) is corrosion electric current density；
The average cross-section A (t) of Corrosion Reinforcement may be expressed as:
A (t)=π D2(t)/4 (3)
The yield strength of (1-2) Corrosion Reinforcement accumulates directly related, Corrosion Reinforcement yield strength and corrosion degree with its remaining cross-section It is approximate in a linear relationship, it may be expressed as:
In formula, fy0For unattacked reinforcement yielding intensity；fyIt (t) is Corrosion Reinforcement yield strength；αyFor Corrosion Reinforcement strength degradation system Number, takes αy=0.9；A0For unattacked reinforcing steel area；
When (1-3) reinforced beam is reached yield strength by shear-steel muscle, the active force of reinforcing bar be may be expressed as: at diagonal crack
Tx=A (t)eff,xf(t)yc,x (5)
Ty=A (t)eff,yf(t)yc,y (6)
Tob=A (t)eff,obf(t)yc,ob (7)
In formula, Tx、TyAnd TobThe pulling force of respectively vertical muscle, stirrup and diagonal bar；f(t)yc,x、f(t)yc,yWith f (t)yc,obIt is respectively vertical The yield strength of muscle, stirrup and diagonal bar；A(t)eff,x、A(t)eff,yWith A (t)eff,obThe section of respectively vertical muscle, stirrup and diagonal bar Product.
3. aged reinforced concrete beam bridge shear-carrying capacity evaluation method according to claim 1, which is characterized in that the step Suddenly (2) are further comprising the steps of:
(2-1) assumes diagonal crack top depth of compressive zone csConcrete compressive strain is ε, the point to natural axis at arbitrary point in range Distance be x；According to plane cross-section assumption, then csThe horizontal compressive strain ε of range inner concrete are as follows:
In formula, ε0And εcThe respectively corresponding strain (ε of concrete peak stress0=0.002) compression edge and at the top of beams of concrete Strain；h0For the effective cross-section height of beam；x0For the corresponding depth of section of concrete peak stress.ε'xMuscle is indulged for pure bending to answer Become, calculated as the following formula:
In formula, EsTo indulge muscle elasticity modulus；M and P is the moment of flexure and shearing for calculating section；α is Diagonal crack and horizontal vertical muscle Inclination angle.Then back concrete compression side strain indicates are as follows:
Concrete compression strain-stress relation are as follows:
In formula, coefficient n=2- (fcu,k- 50)/60, as n > 2, n=2 is taken；fcu,kFor compressive strength of concrete standard Value；fcFor concrete axial compressive strength design value；εcuFor the ultimate compressive strain of concrete of normal section；
(2-2) integrates the non-cracked concrete section in critical diagonal crack top, then compressive region concrete resultant force size are as follows:
In formula, b is deck-siding；
Active force C to diagonal crack top distance are as follows:
Square is taken to critical diagonal crack lower end concrete triangle isolation body unit VT position, is had
In formula, β is the angle of diagonal bar and stirrup；Depth of compressive zone when c is beam pure bending；TfTo indulge muscle active force at bending cracks；
Being rounded a curved scissors region is slider, compressive region concrete point of resultant force C when to pure bendingfSquare is taken, is had:
Tf=Ra/d (15)
In formula, R is end reaction；A is horizontal distance of the load(ing) point to support；D is to indulge muscle to CfThe vertical range of position；
Square is taken to critical diagonal crack upper end triangle isolation body unit active force C point, is had:
In formula, z is distance of the critical diagonal crack top to depth of compressive zone point of resultant force；
It is taken as firmly CfDistance of the point away from beam top edge is 0.4c, then c/h0≈ 0.5, tan α ≈ a/h0, d/h0≈1-0.4c/h0, It can obtain:
It enablesDiagonal crack top concrete compression area height can be obtained are as follows:
4. aged reinforced concrete beam bridge shear-carrying capacity evaluation method according to claim 1, which is characterized in that the step Suddenly (3) are further comprising the steps of:
Based on ultimate shear balance theory, by beam Diagonal crack upper left side slider unit horizontal direction stress balance relationship, Have:
C-Tx-Tobβ=0 sin (19)
Further, indulging muscle amount of force indicates are as follows:
When shear compression failure occurs for reinforced beam, R=Vu, ultimate shear bearing capacity formula are as follows:
Vu=α1A(t)eff,yf(t)yc,y+α2A(t)eff,obf(t)yc,ob+α3fcbcs (21)
5. aged reinforced concrete beam bridge shear-carrying capacity evaluation method according to claim 1, which is characterized in that this method It is further comprising the steps of:
By determining steel bar corrosion initial time, Corrosion Reinforcement sectional area, Corrosion Reinforcement yield strength, diagonal crack top compressive region Height csAnd its size and location of range inner concrete horizontal applied force C, the then shearing resistance that rc beam bridge can be obtained are held Carry power Vu。
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CN112464345A (en) * 2020-11-26 2021-03-09 北京工业大学 Deformation-based seismic damage reinforced concrete column crack width calculation method
CN112464345B (en) * 2020-11-26 2024-02-02 北京工业大学 Earthquake damage reinforced concrete column crack width calculation method based on deformation
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CN114510767B (en) * 2022-02-22 2022-09-02 中交第四公路工程局有限公司 Steel structure assembly effect evaluation method and system based on three-dimensional modeling
CN116305414A (en) * 2023-01-19 2023-06-23 安徽省交通控股集团有限公司 Shear design method and device based on wedge-shaped section shear model
CN116305414B (en) * 2023-01-19 2024-05-28 安徽省交通控股集团有限公司 Shear design method and device based on wedge-shaped section shear model

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