CN108830022A - Based on steel strand wires adhesion strength prediction technique under rotation and protective layer Cracking Failure - Google Patents
Based on steel strand wires adhesion strength prediction technique under rotation and protective layer Cracking Failure Download PDFInfo
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Abstract
It is disclosed by the invention to be based on steel strand wires adhesion strength prediction technique under rotation and protective layer Cracking Failure, establish the relational expression of ultimate bond stress Yu bonding failure face radial stress, the radial stress in bonding failure face when determining concrete splitting bonding failure, it determines that concrete splitting fails and rotates the critical radial stress in bonding failure face when failure changes to drawing, determine the minimum thickness of concrete cover under critical radial compressive stress, assessment is compared to the method for the present invention by existing drawing experimental data relevant to steel strand wires, in conjunction with two kinds of failure modes, verify the precision of the method for the present invention.Consider the rotation bonding mechanism for driving spiral structure and steel strand wires processed away of steel strand wires, can the effectively single prestress wire of simulation and forecast and concrete under two kinds of failure modes, ultimate bond stress i.e. under concrete splitting failure and drawing rotation failure, and there is preferable precision；Improve the deficiency about prestress wire and the research of concrete theory adhesive model.
Description
Technical field
The present invention relates to steel strand wires ultimate bond stress calculation method technical fields, more particularly to one kind based on rotation and to protect
Steel strand wires adhesion strength prediction technique under sheath Cracking Failure.
Background technique
As prestressed reinforced concrete construction is widely used in each large-engineering, safety problem is also increasingly highlighted.Prestressing force
Adhesive property between muscle and concrete is an important factor for influencing structure safe handling.Bonding between steel strand wires and concrete is main
It is realized by the shearing force between the two contact surface.The interface stress is complicated, by concrete strength, protective layer thickness, reinforcing bar
Diameter and steel strand surface feature etc. influence.It is less for the research of the adhesive model of steel strand wires and concrete at present, it is most of
Concentrate on regular reinforcement.Prestress wire is mostly twisting spiral structure, this twisting steel strand wires adhesive property and regular reinforcement
Necessarily it is not quite similar.
Adhesion strength model research between existing steel strand wires and concrete is mostly based on experiment to be unfolded, prediction result pair
Experiment condition degree of dependence is higher, in practical projects using limited.Some scholars by steel strand wires construction simplified with
And it is theoretically studied by the methods of finite element modelling.Silk outside steel strand wires is reduced at a certain angle by traditional technology
It is spirally looped around the rib on internal thread surface, it is strong to establish in ground anchor structure the bonding of steel strand wires and cement slurry under different side pressures
Spend model.However, not there is adhesion strength model viscous due to rotating caused by its twisting construction when can consider steel strand wires stress at present
Influence of the mechanism to ultimate bond stress is tied, corresponding adhesion strength mechanical model waits to develop.
Summary of the invention
The purpose of the present invention is to provide one kind to be predicted based on steel strand wires adhesion strength under rotation and protective layer Cracking Failure
Method, effectively solution above-mentioned technical problem.
Effectively to solve above-mentioned technical problem, technical solution of the present invention is as follows：
Based on steel strand wires adhesion strength prediction technique under rotation and protective layer Cracking Failure, this approach includes the following steps：
(1) relational expression of ultimate bond stress Yu bonding failure face radial stress is established：Consider steel strand surface
Spiral structure feature, based on the stress balance on its outer silk rib surface during the drawing process, to concrete splitting failure and drawing
The relationship between ultimate bond stress and bonding failure face radial stress under rotation two kinds of failure modes of failure is derived；
(2) radial stress in bonding failure face when determining concrete splitting bonding failure：According in steel strand wires loading process
The relationship of contact surface concrete radial displacement and radial stress, reinforcing bar outer concrete is regarded as caused by being slided by steel strand wires rib
It is heavy wall cylindrical body, considers that steel strand wires surrounding concrete does not crack caused by bonding, part cracking and three ranks of instant of complete cracking
Section, the radial stress in bonding failure face when determining concrete splitting bonding failure；
(3) it determines that concrete splitting fails and rotates the critical radial stress in bonding failure face when failure changes to drawing：Root
Stress characteristic when failure is rotated according to steel strand wires, establishes the moment of flexure stress balance relationship based on steel strand wires center, and accordingly
Derive the critical radial stress in bonding failure face when rotating failure conversion to drawing from concrete splitting damage inactivation；
(4) the minimum thickness of concrete cover under critical radial compressive stress is determined：According in steel strand wires loading process by
The relationship of contact surface concrete radial displacement and corresponding radial stress, it is maximum to establish steel strand surface rib caused by steel strand wires rib
The relationship of radial stress and thickness of concrete cover, concrete strength etc., and then be derived by under fixing concrete intensity most
Small thickness of concrete cover；
(5) model is verified：The method of the present invention is compared by existing drawing experimental data relevant to steel strand wires and is commented
Estimate, in conjunction with two kinds of failure modes, verifies the precision of the method for the present invention.
Particularly, the step (1) is further comprising the steps of：
First against any lay pitch of steel strand wires, it is divided into the differentiation element of longitudinal multiple equal lengths, it is right later
The mechanical snap power for acting on unit steel strand surface is analyzed, according to stress balance principle to steel strand surface mechanical snap
Effective forced area of power is integrated, and derives pulling capacity and glue that single prestress wire differentiation element length provides accordingly
The relationship for tying failure surface radial stress, is finally evenly distributed on stress surface for pulling capacity and obtains ultimate bond stress and bonding failure
The relational expression of face radial stress；
Derivation in the step (1) about adhesion strength and the relationship of bonding failure face radial stress is specific as follows：
The bonding of steel strand wires and concrete is in the nature the shearing force between contact surface, and bond stress τ b is represented by formula (1)：
τb=Fb/(k·π·d·lb)
In formula, Fb and d are respectively the pulling force and nominal diameter of steel strand wires；Lb is bond length；K is the outer of consideration steel strand wires
The perimeter sampling factor that surface structure introduces can use 4/3；
Steel strand wires longitudinal direction dz length is taken, corresponding cross section rotation angle is d α, the folder of outer silk rib and longitudinal direction at this time
Angle is δ, analysis steel strand wires rib provide bite force forced area, can approximation regard six imperfect crescent as, it is assumed that every steel
The outer silk stress of twisted wire is identical, take wherein any one outer silk crescent analyzed, effective angle of coverage of imperfect crescent
For θ, value range is [0,2 π/3], and the area dA in the region d θ on steel strand wires rib is represented by formula (2)：
DA=hr/sinδ·db/2·dθ
In formula, hr is the height of cross rib；Db is the outer silk diameter of steel strand wires, carries out force analysis to inclined surface dA；
The cohesive force acted on the dA of rib surface is made of shearing force dFv and frictional force dFf；
Wherein, shearing force dFv is parallel to rib surface, and there are an angle of frictions with rib normal to a surface direction by frictional force dFf
φ, it is assumed that the unit cohesive force between steel strand wires and concrete is fcoh, and the direct stress acted in shear fails plane is fn, then
DFv and dFf can be expressed as formula (3), (4)：
dFv=fcohdA
Shearing force dFv and frictional force dFf is decomposed into the parallel force dFb for being parallel to steel strand wires axial direction and perpendicular to axial direction
The following formula of radiation power dFsp (5), (6)：
There are six faces to provide parallel force and circumferential force in total for every steel strand wires, therefore, longitudinal pulling capacity Fb table within the scope of dz
It is shown as formula (7), (8)：
Formula (7) and formula (8) are combined and obtain the expression formula (9) of Fb within the scope of dz：
Fb substitution formula (1) is obtained into adhesion strength τ b expression formula (10) within the scope of dz：
Particularly, the step (2) is further comprising the steps of:
In the step (2), the calculating of the radial stress in bonding failure face, specific steps when concrete splitting bonding failure
For：
Regard reinforcing bar outer concrete as heavy wall cylindrical body, considers that concrete does not crack during the drawing process, portion is separated
It splits and instant of complete cracking three phases, the bilinearity tensile stress degradation model after cracking in conjunction with concrete in tension obtains fn not same order
The expression formula of section：
It does not crack the stage, the relational expression (11) of tangential stress σ t, r and fn at radius r：
In formula, ri and re are respectively the interior of cylindrical body, outer radius；
The fn in part cracking stage consists of two parts, including part of not crackingWith cracking partFor not opening
Part concrete is split, linear elastic materials are seen as, for the part concrete that cracks, is considered soft under concrete in tension state
Change behavior, and introduce Virtual gauge.The expression formula for obtaining part cracking stage fn is following (12)：
In formula, rcr is the radius in crack occurrence forward position；Rs=d/2 is steel strand wires nominal radius；Ec is concrete elastic mould
Amount；ε cr=fct/Ec is concrete cracking strain；N is the quantity in virtual crack, assumes n=3 herein；A and b is to indicate coagulation
The constant of soil cracking softening behavior；Maximum crack width when w0 is concrete pulling stress failures, the diameter at the instant of complete cracking stage
It is consistent with the part cracking stage cracking stress of part to stress.
Particularly, the step (3) is further comprising the steps of:
In the step (3), concrete splitting, which fails, rotates the critical radial direction in bonding failure face when failure changes to drawing
The calculating of stress, the specific steps are：
The power Fribv for being decomposed into vertical splitting plane of the component Frib of steel strand wires longitudinal direction and it is parallel to splitting plane
Power Fribh；
Power Fribv expression (13) perpendicular to splitting plane is as follows：
It is parallel to the power Fribh of splitting plane, expression formula (14) is as follows：
Therefore Frib can be expressed as (15)：
The relational expression (16) of fn and torque Mrib within the scope of dz can be obtained by centering silk calculated torque：
Next the peak torque Mmax for asking concrete friction power to provide, peak torque Mmax are represented by (17)：
In formula, μ=tan (φ) is coefficient of friction；
Ignore silk diameter difference inside and outside steel strand wires, i.e. da=db, then expression formula (18)：
When Mrib reaches Mmax, steel strand wires reach rotation critical state, hereafter continuing growing with pulling capacity, and steel twists
Line starts to rotate, and reaches maximum bonded stress；Reach fn when maximum bonded stress, max can pass through formula (17) and formula (18) phase
Etc. obtaining, the critical compressive stress fn when rotation of contact interface steel strand wires is obtained, shown in crit following expression (19)：
Beneficial effects of the present invention are：It is provided by the invention strong based on steel strand wires bonding under rotation and protective layer Cracking Failure
Prediction technique is spent, considers the rotation bonding mechanism for driving spiral structure and steel strand wires processed away of steel strand wires, it can effective simulation and forecast list
The pole of root prestress wire and concrete under two kinds of failure modes, i.e., under concrete splitting failure and drawing rotation failure
Adhesion strength is limited, and there is preferable precision；It improves about prestress wire and the research of concrete theory adhesive model
It is insufficient.
The present invention is described in detail with reference to the accompanying drawing.
Detailed description of the invention
Fig. 1 is length dz schematic diagram.
Fig. 2 is steel strand wires longitudinal direction perspective view.
Fig. 3 is any outer silk of steel strand wires perspective view along longitudinal direction.
Fig. 4 is that the effect on rib surface is tried hard to.
Fig. 5 is the torque diagram of bite force on steel strand wires rib.
Fig. 6 is the peak torque figure that frictional force generates steel strand wires.
Specific embodiment
Embodiment 1：
Referring to shown in Fig. 1 to Fig. 6, the present embodiment implements this method main method and includes：Firstly, considering steel strand wires twisting structure
Feature is made, the stress balance equation under steel strand wires and surrounding concrete constraint is established, steel strand wires adhesion strength is derived and bonding is lost
The relationship of effect face radial stress；Then, concrete splitting destruction and steel strand wires drawing rotation failure are taken into account, two kinds of mistakes are given
Contact surface radial stress calculation expression under effect mode, and then establish the steel strand wires ultimate bond stress under two kinds of failure modes
Theoretical calculation model；Finally, verifying the precision and feasibility of the method for the present invention by existing experimental data.Specific step is as follows：
(1) relational expression of ultimate bond stress Yu bonding failure face radial stress is established：Consider steel strand surface
Spiral structure feature, based on the stress balance on its outer silk rib surface during the drawing process, to concrete splitting failure and drawing
The relationship between ultimate bond stress and bonding failure face radial stress under rotation two kinds of failure modes of failure is derived；
(2) radial stress in bonding failure face when determining concrete splitting bonding failure：According in steel strand wires loading process
The relationship of contact surface concrete radial displacement and radial stress, reinforcing bar outer concrete is regarded as caused by being slided by steel strand wires rib
It is heavy wall cylindrical body, considers that steel strand wires surrounding concrete does not crack caused by bonding, part cracking and three ranks of instant of complete cracking
Section, the radial stress in bonding failure face when determining concrete splitting bonding failure；
(3) it determines that concrete splitting fails and rotates the critical radial stress in bonding failure face when failure changes to drawing：Root
Stress characteristic when failure is rotated according to steel strand wires, establishes the moment of flexure stress balance relationship based on steel strand wires center, and accordingly
Derive the critical radial stress in bonding failure face when rotating failure conversion to drawing from concrete splitting damage inactivation；
(4) the minimum thickness of concrete cover under critical radial compressive stress is determined：According in steel strand wires loading process by
The relationship of contact surface concrete radial displacement and corresponding radial stress, it is maximum to establish steel strand surface rib caused by steel strand wires rib
The relationship of radial stress and thickness of concrete cover, concrete strength etc., and then be derived by under fixing concrete intensity most
Small thickness of concrete cover；
(5) model is verified：The method of the present invention is compared by existing drawing experimental data relevant to steel strand wires and is commented
Estimate, in conjunction with two kinds of failure modes, verifies the precision of the method for the present invention.
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 step (1) is further comprising the steps of：
First against any lay pitch of steel strand wires, it is divided into the differentiation element of longitudinal multiple equal lengths, it is right later
The mechanical snap power for acting on unit steel strand surface is analyzed, according to stress balance principle to steel strand surface mechanical snap
Effective forced area of power is integrated, and derives pulling capacity and glue that single prestress wire differentiation element length provides accordingly
The relationship for tying failure surface radial stress, is finally evenly distributed on stress surface for pulling capacity and obtains ultimate bond stress and bonding failure
The relational expression of face radial stress；
Derivation in the step (1) about adhesion strength and the relationship of bonding failure face radial stress is specific as follows：
The bonding of steel strand wires and concrete is in the nature the shearing force between contact surface, and bond stress τ b is represented by formula (1)：
τb=Fb/(k·π·d·lb)
In formula, Fb and d are respectively the pulling force and nominal diameter of steel strand wires；Lb is bond length；K is the outer of consideration steel strand wires
The perimeter sampling factor that surface structure introduces can use 4/3；
Steel strand wires longitudinal direction dz length is taken, corresponding cross section rotation angle is d α, the folder of outer silk rib and longitudinal direction at this time
Angle is δ, analysis steel strand wires rib provide bite force forced area, can approximation regard six imperfect crescent as, it is assumed that every steel
The outer silk stress of twisted wire is identical, take wherein any one outer silk crescent analyzed, effective angle of coverage of imperfect crescent
For θ, value range is [0,2 π/3], and the area dA in the region d θ on steel strand wires rib is represented by formula (2)：
DA=hr/sinδ·db/2·dθ
In formula, hr is the height of cross rib；Db is the outer silk diameter of steel strand wires, carries out force analysis to inclined surface dA；
The cohesive force acted on the dA of rib surface is made of shearing force dFv and frictional force dFf；
Wherein, shearing force dFv is parallel to rib surface, and there are an angle of frictions with rib normal to a surface direction by frictional force dFf
φ, it is assumed that the unit cohesive force between steel strand wires and concrete is fcoh, and the direct stress acted in shear fails plane is fn, then
DFv and dFf can be expressed as formula (3), (4)：
dFv=fcohdA
Shearing force dFv and frictional force dFf is decomposed into the parallel force dFb for being parallel to steel strand wires axial direction and perpendicular to axial direction
The following formula of radiation power dFsp (5), (6)：
There are six faces to provide parallel force and circumferential force in total for every steel strand wires, therefore, longitudinal pulling capacity Fb table within the scope of dz
It is shown as formula (7), (8)：
Formula (7) and formula (8) are combined and obtain the expression formula (9) of Fb within the scope of dz：
Fb substitution formula (1) is obtained into adhesion strength τ b expression formula (10) within the scope of dz：
The step (2) is further comprising the steps of:
In the step (2), the calculating of the radial stress in bonding failure face, specific steps when concrete splitting bonding failure
For：
Regard reinforcing bar outer concrete as heavy wall cylindrical body, considers that concrete does not crack during the drawing process, portion is separated
It splits and instant of complete cracking three phases, the bilinearity tensile stress degradation model after cracking in conjunction with concrete in tension obtains fn not same order
The expression formula of section：
It does not crack the stage, the relational expression (11) of tangential stress σ t, r and fn at radius r：
In formula, ri and re are respectively the interior of cylindrical body, outer radius；
The fn in part cracking stage consists of two parts, including part of not crackingWith cracking partFor not opening
Part concrete is split, linear elastic materials are seen as, for the part concrete that cracks, is considered soft under concrete in tension state
Change behavior, and introduce Virtual gauge.The expression formula for obtaining part cracking stage fn is following (12)：
In formula, rcr is the radius in crack occurrence forward position；Rs=d/2 is steel strand wires nominal radius；Ec is concrete elastic mould
Amount；ε cr=fct/Ec is concrete cracking strain；N is the quantity in virtual crack, assumes n=3 herein；A and b is to indicate coagulation
The constant of soil cracking softening behavior；Maximum crack width when w0 is concrete pulling stress failures, the diameter at the instant of complete cracking stage
It is consistent with the part cracking stage cracking stress of part to stress.
The step (3) is further comprising the steps of:
In the step (3), concrete splitting, which fails, rotates the critical radial direction in bonding failure face when failure changes to drawing
The calculating of stress, the specific steps are：
The power Fribv for being decomposed into vertical splitting plane of the component Frib of steel strand wires longitudinal direction and it is parallel to splitting plane
Power Fribh；
Power Fribv expression (13) perpendicular to splitting plane is as follows：
It is parallel to the power Fribh of splitting plane, expression formula (14) is as follows：
Therefore Frib can be expressed as (15)：
The relational expression (16) of fn and torque Mrib within the scope of dz can be obtained by centering silk calculated torque：
Next the peak torque Mmax for asking concrete friction power to provide, peak torque Mmax are represented by (17)：
In formula, μ=tan (φ) is coefficient of friction；
Ignore silk diameter difference inside and outside steel strand wires, i.e. da=db, then expression formula (18)：
When Mrib reaches Mmax, steel strand wires reach rotation critical state, hereafter continuing growing with pulling capacity, and steel twists
Line starts to rotate, and reaches maximum bonded stress；Reach fn when maximum bonded stress, max can pass through formula (17) and formula (18) phase
Etc. obtaining, the critical compressive stress fn when rotation of contact interface steel strand wires is obtained, shown in crit following expression (19)：
The another statement of applicant, implementation method and apparatus structure of the invention that the present invention is explained by the above embodiments,
But the invention is not limited to above embodiment, that is, do not mean that the present invention must rely on the above method and structure could be real
It applies.It should be clear to those skilled in the art, any improvement in the present invention, to implementation method selected by the present invention etc.
Effect replacement and addition, the selection of concrete mode of step etc., all of which fall within the scope of protection and disclosure of the present invention.
Claims (4)
1. based on steel strand wires adhesion strength prediction technique under rotation and protective layer Cracking Failure, which is characterized in that this method includes
Following steps：
(1) relational expression of ultimate bond stress Yu bonding failure face radial stress is established：Consider the spiral of steel strand surface
Construction feature rotates concrete splitting failure and drawing based on the stress balance on its outer silk rib surface during the drawing process
The relationship to fail between the ultimate bond stress under two kinds of failure modes and bonding failure face radial stress is derived；
(2) radial stress in bonding failure face when determining concrete splitting bonding failure：According in steel strand wires loading process by steel
The relationship of contact surface concrete radial displacement and radial stress caused by the sliding of twisted wire rib regards reinforcing bar outer concrete as thick
Wall cylindrical body considers that steel strand wires surrounding concrete does not crack caused by bonding, part cracking and instant of complete cracking three phases, really
Determine the radial stress in bonding failure face when concrete splitting bonding failure；
(3) it determines that concrete splitting fails and rotates the critical radial stress in bonding failure face when failure changes to drawing：According to steel
Twisted wire rotates stress characteristic when failure, establishes the moment of flexure stress balance relationship based on steel strand wires center, and derive accordingly
The critical radial stress in bonding failure face when rotating failure conversion to drawing from concrete splitting damage inactivation；
(4) the minimum thickness of concrete cover under critical radial compressive stress is determined：It is twisted according in steel strand wires loading process by steel
The relationship of contact surface concrete radial displacement and corresponding radial stress, establishes steel strand surface rib maximum radial caused by line rib
The relationship of stress and thickness of concrete cover, concrete strength etc., and then be derived by under fixing concrete intensity minimum mixed
Solidifying protective soil layer thickness；
(5) model is verified：Assessment is compared to the method for the present invention by existing drawing experimental data relevant to steel strand wires, is tied
Two kinds of failure modes are closed, the precision of the method for the present invention is verified.
2. special according to claim 1 based on steel strand wires adhesion strength prediction technique under rotation and protective layer Cracking Failure
Sign is that the step (1) is further comprising the steps of：
First against any lay pitch of steel strand wires, it is divided into the differentiation element of longitudinal multiple equal lengths, later to effect
It is analyzed in the mechanical snap power of unit steel strand surface, according to stress balance principle to steel strand surface mechanical snap power
Effective forced area is integrated, and derives pulling capacity and bonding mistake that single prestress wire differentiation element length provides accordingly
Pulling capacity is finally evenly distributed on stress surface and obtains ultimate bond stress and bonding failure face diameter by the relationship of effect face radial stress
To the relational expression of stress；
Derivation in the step (1) about adhesion strength and the relationship of bonding failure face radial stress is specific as follows：
The bonding of steel strand wires and concrete is in the nature the shearing force between contact surface, and bond stress τ b is represented by formula (1)：
τb=Fb/(k·π·d·lb)
In formula, Fb and d are respectively the pulling force and nominal diameter of steel strand wires；Lb is bond length；K is the outer surface for considering steel strand wires
The perimeter sampling factor introduced is constructed, can use 4/3；
Steel strand wires longitudinal direction dz length is taken, corresponding cross section rotates angle for d α at this time, and the angle of outer silk rib and longitudinal direction is
δ, analysis steel strand wires rib provide bite force forced area, can approximation regard six imperfect crescent as, it is assumed that every steel strand wires
Outer silk stress is identical, take wherein any one outer silk crescent analyzed, effective angle of coverage of imperfect crescent is θ,
Value range is [0,2 π/3], and the area dA in the region d θ on steel strand wires rib is represented by formula (2)：
DA=hr/sinδ·db/2·dθ
In formula, hr is the height of cross rib；Db is the outer silk diameter of steel strand wires, carries out force analysis to inclined surface dA；
The cohesive force acted on the dA of rib surface is made of shearing force dFv and frictional force dFf；
Wherein, shearing force dFv is parallel to rib surface, and there are an angle of friction φ with rib normal to a surface direction by frictional force dFf, false
If unit cohesive force between steel strand wires and concrete is fcoh, the direct stress acted in shear fails plane is fn, then dFv with
DFf can be expressed as formula (3), (4)：
dFv=fcohdA
Shearing force dFv and frictional force dFf is decomposed into the parallel force dFb for being parallel to steel strand wires axial direction and puts perpendicular to axial
Penetrate the following formula of power dFsp (5), (6)：
There are six faces to provide parallel force and circumferential force in total for every steel strand wires, and therefore, longitudinal direction pulling capacity Fb is expressed as within the scope of dz
Formula (7), (8)：
Formula (7) and formula (8) are combined and obtain the expression formula (9) of Fb within the scope of dz：
Fb substitution formula (1) is obtained into adhesion strength τ b expression formula (10) within the scope of dz：
3. special according to claim 1 based on steel strand wires adhesion strength prediction technique under rotation and protective layer Cracking Failure
Sign is that the step (2) is further comprising the steps of:
In the step (2), the calculating of the radial stress in bonding failure face when concrete splitting bonding failure, the specific steps are：
Regard reinforcing bar outer concrete as heavy wall cylindrical body, consider that concrete does not crack during the drawing process, part cracking and
Instant of complete cracking three phases obtain fn different phase in conjunction with the bilinearity tensile stress degradation model after concrete in tension cracking
Expression formula：
It does not crack the stage, the relational expression (11) of tangential stress σ t, r and fn at radius r：
In formula, ri and re are respectively the interior of cylindrical body, outer radius；
The fn in part cracking stage consists of two parts, including part of not crackingWith cracking partFor non-cracking unit
Divide concrete, be seen as linear elastic materials, for the part concrete that cracks, considers the softening row under concrete in tension state
For, and introduce Virtual gauge.The expression formula for obtaining part cracking stage fn is following (12)：
In formula, rcr is the radius in crack occurrence forward position；Rs=d/2 is steel strand wires nominal radius；Ec is modulus of elasticity of concrete；ε
Cr=fct/Ec is concrete cracking strain；N is the quantity in virtual crack, assumes n=3 herein；A and b is to indicate that concrete is opened
Split the constant of softening behavior；Maximum crack width when w0 is concrete pulling stress failures, the radial direction at the instant of complete cracking stage are answered
Power is consistent with the part cracking stage cracking stress of part.
4. special according to claim 1 based on steel strand wires adhesion strength prediction technique under rotation and protective layer Cracking Failure
Sign is that the step (3) is further comprising the steps of:
In the step (3), concrete splitting, which fails, rotates the critical radial stress in bonding failure face when failure changes to drawing
Calculating, the specific steps are：
The power Fribv for being decomposed into vertical splitting plane of the component Frib of steel strand wires longitudinal direction and the power for being parallel to splitting plane
Fribh；
Power Fribv expression (13) perpendicular to splitting plane is as follows：
It is parallel to the power Fribh of splitting plane, expression formula (14) is as follows：
Therefore Frib can be expressed as (15)：
The relational expression (16) of fn and torque Mrib within the scope of dz can be obtained by centering silk calculated torque：
Next the peak torque Mmax for asking concrete friction power to provide, peak torque Mmax are represented by (17)：
In formula, μ=tan (φ) is coefficient of friction；
Ignore silk diameter difference inside and outside steel strand wires, i.e. da=db, then expression formula (18)：
When Mrib reaches Mmax, steel strand wires reach rotation critical state, hereafter continuing growing with pulling capacity, and steel strand wires are opened
Begin to rotate, reaches maximum bonded stress；Reach fn when maximum bonded stress, max can be obtained by the way that formula (17) is equal with formula (18)
It arrives, shown in critical compressive stress fn, the crit following expression (19) when obtaining the rotation of contact interface steel strand wires：
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| CN111811937A (en) * | 2020-07-08 | 2020-10-23 | 山东大学 | Method for pre-judging failure mode of geosynthetic material in sandy soil |
| CN112613103A (en) * | 2020-12-22 | 2021-04-06 | 长沙理工大学 | Method for calculating transfer length of pretensioned member under influence of concrete spalling |
| CN113468640A (en) * | 2021-06-29 | 2021-10-01 | 中铁十四局集团有限公司 | Method for obtaining drawing force of main rib of split type connecting piece |
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| CN113468640A (en) * | 2021-06-29 | 2021-10-01 | 中铁十四局集团有限公司 | Method for obtaining drawing force of main rib of split type connecting piece |
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| CN108830022B (en) | 2022-10-25 |
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