CN105550419B - FRP cloth reinforces the calculation method of the ultimate bearing capacity of pier grafting column - Google Patents
FRP cloth reinforces the calculation method of the ultimate bearing capacity of pier grafting column Download PDFInfo
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Abstract
The invention proposes the calculation method that a kind of FRP cloth reinforces the ultimate bearing capacity of pier grafting column, FRP cloth reinforces pier grafting column as hoop, and the ultimate bearing capacity of the pier grafting column is calculated as follows:Wherein: NuIndicate the ultimate bearing capacity of the pier grafting column;R indicates the radius of the cross section of the pier grafting column;γ indicates the strength reduction factor of the pier grafting column;σcIndicate the axial compressive strength without constraint column;The constraint strength coefficient of β expression confined wood column;ξ indicates that name matches cloth rate;T indicates hoop thickness;μ0Indicate broad sense Bai Song ratio;εuIndicate the compressive ultimate strain of timber;EfIndicate the elasticity modulus of hoop.The present invention provides reasonable theoretical direction for the design for reinforcing pier grafting column using FRP cloth, more particularly to consider hoop position and hoop width, ensure that the pier grafting column reinforced in this way can reach design requirement.
Description
Technical field
The invention belongs to pier grafting column reinforcement technique fields, are related to a kind of calculation method of ultimate bearing capacity, especially ring
Bind round the calculation method of the ultimate bearing capacity for the pier grafting column reinforced.
Background technique
In timber buildings, pillar as main supporting member, failure mode be mainly shown as it is rotten, damage by worms,
Cracking etc..From the point of view of the result of field research, the corrosion of pillar occurs mainly in pillar root, the column at house cornice
End.For this destruction, usually repaired using the method that pier connects.
Traditional reinforcement means that hoop ironware is still widely used is reinforced currently, connecing for the pier of ancient building, tradition is reinforced
Ironware there is corrosion, and iron hoop size used is generally only determined by the experience of master worker, lacks reason
By foundation.Using fiber cloth reinforced pier grafting column first is that corrosion problem is not present, second is that convenient and quick construction, third is that reinforcing safety
Reliably, therefore possess vast potential for future development.
Currently, being applied to the reinforcing research of timber structure column class component to FRP (fibre reinforced composites) material both at home and abroad
It also compares less, related some researchs are also concentrated mainly on the hoop that research relies on CFRP (carbon fibre reinforced composite)
Effect reinforces whole and is damaged column, to improve the rigidity and ultimate bearing capacity of column class component, reinforces pier for CFRP and connects grinding for column
Study carefully almost without.In the prior art, the correlation theory for reinforcing pier grafting column without reference to FRP cloth instructs, and is more a lack of and is considering
Pier connects the influence to bearing capacity, and considers that the pier grafting post pole on the basis of hoop position and hoop width limits Design of Bearing Capacity
Theoretical direction.
Summary of the invention
The purpose of the present invention is to provide a kind of in the influence for considering that pier connects to bearing capacity, and considers hoop position and hoop
The method that FRP cloth reinforces the ultimate bearing capacity of pier grafting column is calculated on the basis of width.
In order to achieve the above object, solution of the invention is:
A kind of calculation method of the ultimate bearing capacity of FRP cloth reinforcing pier grafting column, the FRP cloth is as hoop, to described
Pier grafting column is reinforced, and the ultimate bearing capacity of the pier grafting column is calculated as follows:
Wherein: NuIndicate the ultimate bearing capacity of the pier grafting column;
R indicates the radius of the cross section of the pier grafting column;
γ indicates the strength reduction factor of the pier grafting column;
σcIndicate the axial compressive strength without constraint column;
The constraint strength coefficient of β expression confined wood column;
ξ indicates that name matches cloth rate;
T indicates hoop thickness;
μ0Indicate broad sense Bai Song ratio;
εuIndicate the compressive ultimate strain of timber;
EfIndicate the elasticity modulus of hoop.
The strength reduction factor γ and constraint strength factor beta of the pier grafting column are obtained by the method for test fitting.
The broad sense Bai Song ratio μ0Equal to the ratio of the longitudinal strain of the transverse strain and pin of FRP cloth.
Name is calculated as follows with cloth rate:
Wherein, bfIndicate the width of hoop;The spacing of s expression hoop.
The width b of the hoopfCalculation method the following steps are included:
(1) b is enabledf=0, N is found out according to the following formula1:
Wherein: N1Indicate that pier connects the resultant force that section top hoop acts on left half of pin;
FmaxIndicate the maximum shear of column lower end;
h1Indicate that pier connects height, i.e., along the distance to stone base of column stone top end face on pier interface;
h3Indicate the distance between twice hoop point of resultant force up and down;
A indicates the distance at hoop edge to pier interface;
(2) the smallest whole ten number for meeting following two formulas, the width b as temporary hoop are askedf:
Wherein: fyIndicate the ultimate strength of hoop;
(3) the width b for the temporary hoop for acquiring the step (2)fIn generation, returns following formula, seeks N at this time1;
(4) N for acquiring the step (3)1Following formula review is substituted into, if meeting following formula, the step (2) is acquired temporary
When hoop width bfIt can be as the width of actual hoop:
Wherein: I indicates to calculate the moment of inertia in section;The calculating section is on pier interface along left half of pin section;
B indicates the width for calculating section;
fvIndicate timber shearing-strength of wood along the grain design value;
S indicates the area moment of the sectional area to neutral axis of calculating or more.
The width b of the hoopfCalculation method further include step (5): if in the step (4) not by review,
It returns again to the step (1) to recalculate, and increases the width b of hoop in the step (1)fPreset value.
Increase the width b of the hoop in the step (1) in the step (5)fPreset value increment according to the straight of column
Depending on diameter.
Increase the width b of the hoop in the step (1) in the step (5)fPreset value increment be 30~
100mm。
The FRP cloth is CFRP cloth.
By adopting the above scheme, the beneficial effects of the present invention are: the invention proposes a kind of FRP cloths to reinforce pier grafting column
Ultimate bearing capacity calculation method, for using FRP cloth reinforce pier grafting column design provide reasonable theoretical direction, especially
It can be considered that hoop position and hoop width, ensure that the pier grafting column reinforced in this way can reach design requirement.
Detailed description of the invention
Fig. 1 is that CFRP reinforces pin sidewise restraint analysis schematic diagram in the embodiment of the present invention;
Fig. 2 is the schematic diagram of CFRP hoop dimension in the embodiment of the present invention;
Fig. 3 a is that pier connects one of calculating schematic diagram of section in the embodiment of the present invention;
Fig. 3 b is the two of the calculating schematic diagram that pier connects section in the embodiment of the present invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings.
In the present embodiment, FRP cloth uses CFRP cloth, is used as hoop, adds instead of conventional ironware to pier grafting column
Gu.According to Richart model method, the compression strength of confined wood column can be expressed as following formula:
σ=σc+βσr (1)
Wherein: σ is the axial compressive strength of pin after constraint;σcFor the axial compressive strength without constraint column;β is about beam intensity
Spend coefficient;σrIt is hoop to the hoop constraint power of pin.
And in fact, pin is actually two parts of disconnection due to the presence that pier connects, interface is weakened.In axle center
In loading procedure, the factors such as accidental bias all can cause pier interface to have the tendency that opening, and the bearing capacity for making pier connect column is less than log.
In order to consider that this pier connects the reduction of bring axis of a cylinder heart bearing capacity, the application improves above-mentioned Richart model, obtains about
The compression strength of Shu Muzhu such as following formula:
σ=γ σc+βσr (2)
Wherein: γ indicates that pier connects column strength reduction factor.
Fig. 1 is that CFRP reinforces pin sidewise restraint analysis schematic diagram in the present embodiment, can be obtained by the force analysis to X-direction
To following formula:
Wherein: the angle of θ expression integral unit and coordinate axis origin line and X-axis;
R indicates the radius of the cross section of pin;
The thickness of t expression CFRP hoop;
σfIndicate the tensile stress of CFRP hoop.
Above formula is integrated to obtain:
Wherein: εfIndicate the strain of hoop;
EfIndicate the elasticity modulus of hoop.
When CFRP is non-to be abound with, the width of hoop is bf, the spacing of hoop is s, and the length that pier connects section is h, each
The Payload area of hoop is (bf+ s), as shown in Fig. 2, therefore formula (3) becomes following formula:
Above formula is integrated to obtain:
It tends not to play a role well experiments have shown that pasting two layers of carbon cloth, many times has no bearing capacity
It further increases.In the calculating of the application, the raising effect of multi-storey up-down and translation is not considered, it is believed that the carbon fiber to play a role
Cloth is first layer carbon cloth, this is a kind of full calculation method content to retain sovereignty over a part of the country.
Sometimes the hoop maximum stretching strain of carbon cloth is not readily available, but it can be seen from the experiment that, the maximum of hoop is drawn
Strain is consistent with the maximum stretching strain deformation on pin with position timber, but there are hysteresis for the strain of fiber hoop.It can be with
Think εf=k εt, and εt=-μ εl, wherein εtFor the transverse strain of pin, εlFor longitudinal compressive strain of pin, μ is pin
Poisson's ratio, k are the response lag coefficient of hoop.Reach capacity bearing capacity when, longitudinal compressive strain reaches maximum compressive strain εu.It is fixed
Adopted calculating parameterThis is the parameter of a reaction hoop reinforcing amount, reflects hoop reinforcing pier indirectly and connects column
With cloth rate, the application is referred to as name and matches cloth rate ξ.Wherein, bfIndicate the width of hoop.On this basis, formula (6) are substituted into formula
(2) it obtains:
Calculation method according to the bearing capacity of the available CFRP cloth pier grafting column of formula (7) can be:
Wherein: NuIndicate the bearing capacity of CFRP cloth pier grafting column;
The sectional area of A expression pin;
The constraint strength coefficient of β expression confined wood column;
ξ indicates that name matches cloth rate, can be by formulaIt calculates;Size is equal to hoop width than upper hoop width and ring
Bind round the sum of spacing;
μ0Indicate broad sense Bai Song ratio;
εuIndicate the compressive ultimate strain of timber.
In formula (8), unknown quantity be parameter γ, β, k, by many experiments be fitted determine constant γ, β, k, value, can obtain
To the Ultimate Strength formula of confined wood column.K can be strained by hoop position hoop and the ratio of timber strain obtains,
Experimental data can be substituted into fitting and be obtained by γ and β by bearing capacity formula, other parameters can be tested by material etc.
It arrives.K μ can also be write as to a constant μ0, μ0Physical significance be the transverse strain of carbon fiber hoop and the longitudinal strain of timber
Ratio is referred to as generalized Poisson ratio in the application.
The width b of hoopfFor design value, can be obtained on the basis of the force analysis to pin.Since pillar majority is
" flat pendulum floating puts " be placed in above stone base of column stone, after column lower end horizontal force reaches a certain level, lateral sliding will occur for pillar,
Therefore the maximum shear of column lower end are as follows:
Fmax=μ N (9)
Wherein: FmaxIndicate the maximum shear of column lower end;
μ indicates the coefficient of friction between column and stone base of column stone, can be determined by related experiment, size 0.3~0.5 it
Between.
Fig. 3 a and Fig. 3 b are the calculating schematic diagram that pier connects section, wherein h1Height is connect for pier, i.e., along to column on pier interface
The distance of the stone base of a column top end face;h2For pier interface lower edge to the distance of stone base of column stone top end face;Δ h is that pier connects segment length;h3It is upper and lower two
Distance between road hoop point of resultant force.When the width of hoop is smaller, Δ h=h can be approximately considered3, but when hoop width compared with
Greatly, the width of hoop cannot be ignored when binding round using CFRP, at this time Δ h=h3+bf+2a。bfFor hoop width, a is hoop edge to pier
The distance of interface can choose the patch mode of a=0 according to the design needs.
Pier meets height h1Determination and FmaxRelated, on pier interface along section, which is seriously undermined, bending resistance
The only half of pin section of bearing capacity undertakes, which becomes controlling sections.The section turn moment are as follows:
MOn=Fmaxh1 (10)
The Ultimate Bearing Capacity in the section is the anti-bending bearing capacity of semi-circular cross-section, it may be assumed that
Mu=MOn=Wnfm (11)
Wherein: WnIndicate the composite bending modulus of pin semi-circular cross-section;
fmIndicate the bending strength of timber.
It is hereby achieved that:
On pier interface along section, shearing is undertaken by the pillar of wherein half, according to " Code for design of timber structures "
(GB50005-2010) 5.2.2 section regulation:
Wherein: V indicates the shearing that pin is born;
Area moment of the sectional area of S expression or more to neutral axis;
I indicates the moment of inertia in calculating section, and the calculating section is on pier interface along left half of pin section;
B indicates to calculate cross-sectional width;
fvIndicate the design value of timber shearing-strength of wood along the grain.
It can thus be concluded that:
Wherein: VuIndicate the ultimate shear that pin can bear.
It can be obtained by the equilibrium relation of power in Fig. 3 a:
Simultaneous acquires:
Wherein: N1Indicate that pier connects section top hoop to the resultant force of left half of pin, as shown in Figure 3a;
N2Indicate that pier connects pars infrasegmentalis hoop to the resultant force of left half of pin, as shown in Figure 3a.
When not designing the width of carbon cloth, bfIt is a unknown quantity, can at this time uses and enable bf=0 method
Carry out tentative calculation, it is to be designed go out carbon cloth dosage after, then generation return formula (18) calculate N1, and checked according to formula (14).
The size of horizontal hoop needs to meet:
ASfy≥N2=Fmax-N1AS (19)
Wherein: ASIndicate the area of hoop;
fyIndicate the ultimate strength of hoop.
ASfy≥N1 (20)
Both direction due to carbon cloth in hoop generates pulling force:
AS=2bft (21)
Therefore:
And
It follows that the width b of hoop can be calculated as followsf:
(1) b is enabledf=0, N is found out according to formula (18)1;
(2) the smallest whole ten number for meeting formula (22) and formula (23), the width b as temporary hoop are askedf:
(3) the width b for the temporary hoop for acquiring step (2)fIn generation, goes back to formula (18), seeks N at this time1;
(4) N for acquiring step (3)1Substitution formula (13) is checked, if meeting formula (13), step (2) acquires temporary
When hoop width bfIt can be as the width of actual hoop;If not returning again to step (1) by review and counting again
It calculates, and increases the width b of hoop in step (1)fPreset value.In the present invention, increase the width b of the hoop in step (1)f's
The increment of preset value is depending on the diameter of column.In the present embodiment, increase the width b of the hoop in step (1)fPreset value
Increment be 30~100mm.
In the present embodiment, hoop uses CFRP cloth, and other FRP cloths also can be used in the present invention.
According to the ultimate bearing capacity of pier grafting column obtained by the above method, correlation theory research and engineer application can be used as
Guidance, the FRP cloth that auxiliary obtains capable of reaching design requirement reinforces pier grafting column.
The design that FRP cloth reinforces pier grafting column is mainly carried out according to following steps, and an economy, reasonable, feasible
Design scheme is generally required by modification calculating can just obtain repeatedly several times:
(1) according to load above column, the maximum axle power for being transmitted to column lower end is calculated;The maximum of column lower end is calculated by formula (9)
Shear Fmax.In situation known to the horizontal shear of column bottom, check formula F≤F is neededmax。
(2) maximum pier is calculated by formula (12) and connect height, judged by the rotten length of live pillar grain: if pillar grain is rotten
Length is greater than the value, then poor rotten length is too long, cannot connect method using pier and be reinforced;If the rotten length of pillar grain is less than or equal to
The value then determines that reasonable pier connects height according to the rotten length of grain of pillar;
(3) length that pier connects section, primary Calculation season b are calculated by formula (17)f=0.It may be otherwise and assume that pier meets segment length
Δ h is spent, finds out N under a proportional relationship1, N is calculated according to formula (18)1Value, and check whether meet N1≤Vu, if being unsatisfactory for
Reinforcement means cannot be connect using pier.
(4) width of hoop is calculated according to formula (22) and formula (23), and guaranteedWhenWhen, pier
Connecing section is to be abound with hoop, at this time h3=bf。
(5) resulting b is calculated according to designf, substitute into formula (17) and checked;
(6) by the hoop width b of designfWhether substitution formula (8), the pillar axial press capacity after calculating design can
It meets the requirements, that is, the pillar axial press capacity calculated is greater than or is equal to design value.
In conclusion the invention proposes the calculation method that a kind of FRP cloth reinforces the bearing capacity of pier grafting column, to use
The design that FRP cloth reinforces pier grafting column provides reasonable theoretical direction, more particularly to consider hoop position and hoop width, protects
Design requirement can be reached by having demonstrate,proved the pier grafting column reinforced in this way.
This hair can be understood and applied the above description of the embodiments is intended to facilitate those skilled in the art
It is bright.Person skilled in the art obviously easily can make various modifications to these embodiments, and described herein
General Principle is applied in other embodiments without having to go through creative labor.Therefore, the present invention is not limited to implementations here
Example, those skilled in the art's announcement according to the present invention, improvement and modification made without departing from the scope of the present invention all should be
Within protection scope of the present invention.
Claims (9)
1. a kind of FRP cloth reinforces the calculation method of the ultimate bearing capacity of pier grafting column, the FRP cloth is as hoop, to the pier
Grafting column is reinforced, it is characterised in that: the ultimate bearing capacity of the pier grafting column is calculated as follows:
Wherein:
NuIndicate the ultimate bearing capacity of the pier grafting column;
R indicates the radius of the cross section of the pier grafting column;
γ indicates the strength reduction factor of the pier grafting column;
σcIndicate the axial compressive strength without constraint column;
The constraint strength coefficient of β expression confined wood column;
ξ indicates that name matches cloth rate;
T indicates hoop thickness;
μ0Indicate broad sense Bai Song ratio;
εuIndicate the compressive ultimate strain of timber;
The elasticity modulus of Ef expression hoop.
2. the calculation method that FRP cloth according to claim 1 reinforces the ultimate bearing capacity of pier grafting column, it is characterised in that:
The strength reduction factor γ and constraint strength factor beta of the pier grafting column are obtained by the method for test fitting.
3. the calculation method that FRP cloth according to claim 1 reinforces the ultimate bearing capacity of pier grafting column, it is characterised in that:
The broad sense Bai Song ratio μ0Equal to the ratio of the longitudinal strain of the transverse strain and pin of FRP cloth.
4. the calculation method that FRP cloth according to claim 1 reinforces the ultimate bearing capacity of pier grafting column, it is characterised in that:
Name is calculated as follows with cloth rate:
Wherein, bfIndicate the width of hoop;
The spacing of S expression hoop.
5. the calculation method that FRP cloth according to claim 4 reinforces the ultimate bearing capacity of pier grafting column, it is characterised in that:
The calculation method of the width bf of the hoop the following steps are included:
(1) b is enabledf=0, N is found out according to the following formula1:
Wherein: N1Indicate that pier connects the resultant force that section top hoop acts on left half of pin;
FmaxIndicate the maximum shear of column lower end;
h1Indicate that pier connects height, i.e., along the distance to stone base of column stone top end face on pier interface;
h3Indicate the distance between twice hoop point of resultant force up and down;
A indicates the distance at hoop edge to pier interface;
(2) the smallest whole ten number for meeting following two formulas, the width b as temporary hoop are askedf:
Wherein: fyIndicate the ultimate strength of hoop;
(3) the width b for the temporary hoop for acquiring the step (2)fIn generation, returns following formula, seeks N at this time1;
(4) N for acquiring the step (3)1Following formula review is substituted into, if meeting following formula, the step (2) is acquired temporary
The width bf of hoop can be as the width of actual hoop:
Wherein: VuIndicate the ultimate shear that pin can bear;
I indicates to calculate the moment of inertia in section;The calculating section is on pier interface along left half of pin section;
B indicates the width for calculating section;
fvIndicate timber shearing-strength of wood along the grain design value;
S indicates the area moment of the sectional area to neutral axis of calculating or more.
6. the calculation method that FRP cloth according to claim 5 reinforces the ultimate bearing capacity of pier grafting column, it is characterised in that:
The calculation method of the width bf of the hoop further includes step (5): if not returning again to institute by review in the step (4)
It states step (1) to recalculate, and increases the width b of hoop in the step (1)fPreset value.
7. the calculation method that FRP cloth according to claim 6 reinforces the ultimate bearing capacity of pier grafting column, it is characterised in that:
Increase the increment of the preset value of the width bf of the hoop in the step (1) in the step (5) depending on the diameter of column.
8. the calculation method that FRP cloth according to claim 6 reinforces the ultimate bearing capacity of pier grafting column, it is characterised in that:
The increment for increasing the preset value of the width bf of the hoop in the step (1) in the step (5) is 30~100mm.
9. the calculation method that FRP cloth according to claim 1 reinforces the ultimate bearing capacity of pier grafting column, it is characterised in that:
The FRP cloth is CFRP cloth.
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CN114294008B (en) * | 2022-01-13 | 2024-03-05 | 辽宁工业大学 | FRP strip constraint and sprayed concrete and geogrid combined coal column reinforcement method |
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JP2002086601A (en) * | 2000-09-14 | 2002-03-26 | Murata Mach Ltd | Laminate structure of frp composition |
CN102912936A (en) * | 2012-10-16 | 2013-02-06 | 浙江树人大学 | Method for designing FRP (fiber reinforce plastic) tube-concrete-steel tube combined column |
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JP2002086601A (en) * | 2000-09-14 | 2002-03-26 | Murata Mach Ltd | Laminate structure of frp composition |
CN102912936A (en) * | 2012-10-16 | 2013-02-06 | 浙江树人大学 | Method for designing FRP (fiber reinforce plastic) tube-concrete-steel tube combined column |
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