CN106354915A - A calculation method of ultimate bending capacity of reinforced severe damage beam with fiber reinforced polymer - Google Patents

Abstract

The invention relates to a calculation method of ultimate bending capacity of reinforced severe damage beam with fiber reinforced polymer, comprising the steps of the geometrical relationship that S1, going through the cross section of beam strain, the material stress- strain relationship, the establishment of mechanical model, calculating the relative compression zone height; S2, reducing the compressive strength of the concrete in the compression zone; S3, adopting the axial compressive strength of the concrete after the reduction, according to the above steps to recalculate the height of the compression zone; S4, calculating the ultimate bending moment; and S5, calculating the ultimate bending load capacity. The invention provides a prediction for the design and research of the ultimate flexural capacity of the RC beam with a single section of the reinforced concrete with a single rib, and saves the measured cost and a lot of test timeso as to make the ultimate bearing capacity of the reinforcement structure design more accurate;accurately calculating the ultimate bending capacity of the reinforced beam, which makes the engineering and technical personnel more accurate and convenient to control the loading process of the fiber reinforced concrete beam; The method has great economic benefit.

Description

A kind of Ultimate Bearing Capacity computational methods of fiber cloth reinforced severe injury beam

Technical field

The present invention relates to structural strengthening field is and in particular to a kind of limit bending resistance of fiber cloth reinforced severe injury beam carries Power computational methods.

Background technology

In recent years, fibre reinforced composites (fiber reinforced polymer, abbreviation frp) are in armored concrete Research in beam reinforcing and application development are rapid.When reinforced concrete structure design error, suffers from fire, earthquake, corrosion Or after fatigue rupture etc., cause Lack of support it may appear that compared with multiple cracking, it is true that also occurring just because of these cracks, people Just can it be carried out reinforcing out reason.Therefore, after research damages, the reinforcing problem of armored concrete beam has larger reality Meaning.

But current reinforcing research is only limited to the armored concrete of normal reinforced concrete beam or minor injury or corrosion Beam, less for the research reinforcing severe injury reinforced beam aspect using frp sheet material.When reinforced concrete structure occurs Design error, suffer from fire, earthquake, corrosion or fatigue rupture etc. after, cause Lack of support it may appear that compared with multiple cracking, true On, also occur just because of these cracks, people just can carry out reinforcing out reason to it.Therefore, armored concrete after research damages The reinforcing problem of beam has larger realistic meaning.

Continuous basalt fiber strengthens composite (basalt fiber reinforced polymer, abbreviation bfrp) It is with pure natural basalt ore as raw material, under high-temperature fusion, a kind of inorganic tencel of wire drawing strengthens composite wood Material, it is excellent to have intensity height, good endurance, fire prevention and an electrical insulation capability, the advantages of acid and alkali resistance and resistance to chemical attack, and price Cheap.Severe injury reinforced beam is reinforced using bfrp there is preferable economic benefit.

Content of the invention

The purpose of the present invention is for deficiency of the prior art, provides a kind of limit of fiber cloth reinforced severe injury beam Anti-bending bearing capacity computational methods, calculate a kind of new way of offer for solving reinforced beam reinforcing after suffering from major injury Footpath, and pass through verification experimental verification, value of calculation and result of the test are coincide good.

For achieving the above object, the invention discloses following technical scheme:

A kind of Ultimate Bearing Capacity computational methods of fiber cloth reinforced severe injury beam, comprise the steps:

The geometrical relationship that s1 is strained by section of beam, the strain-stress relation of material, set up mechanical model, calculate phase To depth of compressive zone

${\mathrm{\ξ}}_n=\frac{-b+\sqrt{b^2-4ac}}{2a}$

In formula, a, b, c are coefficient, are expressed as follows respectively:

A=0.798f_cbh₀ ², b=0.0033e_ba_bh-f_ya_sh₀, c=-0.0033e_ba_bH, wherein, f_cAxle for concrete Heart comprcssive strength, a_sFor the total cross-section area of tension reinforcement, a_bFor the total cross-section area of different numbers of plies bfrp, h₀For section Effective depth, h be beam section height, f_yFor the yield strength of reinforcing bar, e_bElastic modelling quantity for bfrp；

After calculating a, b and c, bring above-mentioned formula into and can calculate depth of compressive zone；

S2 carries out reduction to compressive region concrete axial compressive strength；

S3 adopts the concrete axial compressive strength after reduction, recalculates depth of compressive zone by above-mentioned steps；

S4 calculating limit moment of flexure；

S5 calculating limit anti-bending bearing capacity.

Further, when carrying out depth of compressive zone calculating, specific as follows:

It is believed that the reinforced beam of poisoning injury meets plane section Jiading after reinforcing in calculating process；Reinforcing bar Strain-stress relation is two-part, and after reinforcement yielding, tensile strength takes yield value；The stress-strain of bfrp linearly closes System；Two-part is adopted, the mathematic(al) representation of its strain-stress relation is as follows during concrete axial compression:

${\mathrm{\&sigma;}}_c=\left\{\begin{array}{cc}{f}_c\&lsqb;1-{(1-\frac{{\mathrm{\&epsiv;}}_c^t}{{\mathrm{\&epsiv;}}_0})}^2\&rsqb;& {\mathrm{\&epsiv;}}_c\&le;{\mathrm{\&epsiv;}}_0\\ f_c& {\mathrm{\&epsiv;}}_0<{\mathrm{\&epsiv;}}_c\&le;{\mathrm{\&epsiv;}}_{cu}\end{array}\right.---\left(1\right)$

In formula, σ_cFor compressive strain ε_cThe stress of corresponding concrete；f_cAxial compressive strength for concrete；It is subject to for beam The compressive strain of nip edge concrete；ε₀Reach f for compressive stress_cWhen concrete compressive strain；ε_cuLimit pressure for concrete should Become；When the cubic compressive strength of concrete is not higher than c50, ε₀It is taken as 0.002, ε_cuIt is taken as 0.0033；

Reinforced beam for severe injury post-reinforcing does not consider that when calculating concrete in tension zone acts on, due to Bfrp cloth and bondline thickness compared with deck-molding very little it is believed that the application point of its cross section centre of form is located at the lower limb of beam Place, sets up set relations as follows:

$\frac{1}{\mathrm{\&rho;}}=\frac{{\mathrm{\&epsiv;}}_c^t}{{\mathrm{\&xi;}}_n{h}_0}=\frac{{\mathrm{\&epsiv;}}_s}{(1-{\mathrm{\&xi;}}_n)h_0}=\frac{{\mathrm{\&epsiv;}}_c}{y}=\frac{{\mathrm{\&epsiv;}}_{tb}}{(1-{\mathrm{\&xi;}}_n)h}---\left(2\right)$

In formula, the radius of curvature that ρ reaches capacity during bearing capacity for beams of concrete；Pressure for beam pressurized area edge concrete Strain；ξ_nFor the ratio of concrete compression area height and effective depth of section, i.e. relative height of compression zone；h₀Effective for section Highly；ε_sThe tensile stress sigma of reinforcing bar_sCorresponding strain；ε_cAway from natural axis distance for y at fiber strain；ε_tbFor bfrp cloth tension σ_tbCorresponding strain；H is beam section height；

Severe injury reinforced beam after reinforcing, compressive region concrete be in elastic-plastic phase it is believed thatMeetSevere injury reinforced beam reinforcing bar before reinforcing has been surrendered, and after reinforcing, reinforcing bar is still in yield situation； Bfrp stress-strain during tension linearly changes, and the physical relation obtaining each material in conjunction with above formula is as follows:

${\mathrm{\&sigma;}}_c=f_c,{\mathrm{\&sigma;}}_s=f_y,{\mathrm{\&sigma;}}_{tb}=e_b{\mathrm{\&epsiv;}}_{tb}=e_b\frac{1-{\mathrm{\&xi;}}_n}{{\mathrm{\&xi;}}_n{h}_0}{\mathrm{\&epsiv;}}_c^{t}h---\left(3\right)$

In formula, f_yYield strength for reinforcing bar；e_bElastic modelling quantity for bfrp；

The strain-stress relation formula during concrete compression shown in formula (1) and the geometry shown in formula (2) is applied to close System, tries to achieve the pressure f of compressive region concrete respectively by integral operation_cAnd its application point is to the distance at compressive region concrete edge y_c, as follows:

$f_c=f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})---\left(4\right)$

$y_c={\mathrm{\&xi;}}_n{h}_0\&lsqb;1-\frac{\frac{1}{2}-\frac{1}{12}{\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_c^t}\right)}^2}{1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t}}\&rsqb;---\left(5\right)$

According to stress distribution, axially set up the equation of static equilibrium: ∑ f along beam_x=0, obtain

$f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})-f_y{a}_s-e_b\frac{1-{\mathrm{\&xi;}}_n}{{\mathrm{\&xi;}}_n{h}_0}{\mathrm{\&epsiv;}}_c^t{\mathrm{ha}}_b=0---\left(6\right)$

In formula, a_sTotal cross-section area for tension reinforcement；a_bTotal cross-section area for different numbers of plies bfrp；By public affairs Formula (6) solves and draws ξ_n；

WhenWhen, compressive region concrete is crushed, and section is destroyed, and beam loses bending bearing capacity, to comprcssive strength Grade is not more than the concrete of c50, takesε₀=0.002, and substitute into formula (6), collated

aξ_n ²+bξ_n+ c=0 (7)

Then solution quadratic equation with one unknown can obtain

${\mathrm{\&xi;}}_n=\frac{-b+\sqrt{b^2-4ac}}{2a}---\left(8\right)$

In formula, a, b and c are coefficient, are expressed as follows respectively:

A=0.798f_cbh₀ ², b=0.0033e_ba_bh-f_ya_sh₀, c=-0.0033e_ba_bh (9)

After calculating a, b and c, bring formula (7) into, you can calculate ξ_n；

Then depth of compressive zone x_nFor

x_n=ξ_nh₀(10).

Further, when reduction being carried out to compressive region concrete axial compressive strength, specifically comprise the following steps that

S2.1 damage before reinforcing crackle does not occur in the range of reinforced beam depth of compressive zone when, concrete anti- Compressive Strength takes former strength grade of concrete corresponding axial compressive strength standard value, that is,

f_c=f_ck(11)

When s2.2 is in the range of cracks can spread before reinforcing to damage reinforced beam depth of compressive zone, the resistance to compression of concrete Intensity level is calculated as follows:

f_c=η f_ck(12)

In formula,For the compressive strength decreasing coefficient of damaged concrete, wherein,It is by curved Area 3 crack top to beam top edge minimum range meansigma methodss, l₁、l₂And l₃It is to beam top edge by curved area 3 crack top Minimum range.

Further, during calculating limit moment of flexure, specifically comprise the following steps that

According to stress distribution, torque equilibrium equation: σ m is built with fiber cloth application point_b=0, obtain

$m=f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})\{h-{\mathrm{\&xi;}}_n{h}_0\&lsqb;1-\frac{\frac{1}{2}-\frac{1}{12}{\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_c^t}\right)}^2}{1-\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_c^t}}\&rsqb;\}-f_y{a}_s{a}_s---\left(13\right)$

In formula: a_sThe vertical dimension away from the tension reinforcement cross section centre of form for the fiber cloth；

WhenWhen, compressive region concrete is crushed, and section is destroyed, and beam loses bending bearing capacity；To comprcssive strength Grade is not more than the concrete of c50, takesε₀=0.002, and substitute into formula (13), collated

M=0.798f_cbξ_nh₀(h-0.412ξ_nh₀)-f_ya_sa_s(14)

In formula, ξ_nFor relative height of compression zone f_cAxial compressive strength for concrete；H is beam section height；h₀For section Effective depth；a_sTotal cross-section area for tension reinforcement；f_yYield strength for reinforcing bar；a_sFiber cloth is horizontal away from tension reinforcement The vertical dimension of cross-section centroid.

Further, during calculating limit anti-bending bearing capacity, for three branch load modes, the limit lotus of reinforced beam Load following formula represents:

$p_u=\frac{6m}{l_0}---\left(15\right)$

In formula: l₀Clear span for beam.

A kind of Ultimate Bearing Capacity computational methods of fiber cloth reinforced severe injury beam disclosed by the invention, have following Beneficial effect:

According to bfrp, the present invention reinforces that compressive region concrete when severe injury reinforced beam destroys is crushed, reinforcing bar Feature through surrendering and bfrp is substantially intact, and consider the reduction problem of compressive region concrete crushing strength, establish the limit and resist Curved bearing capacity formula, through checking, value of calculation and result of the test are coincide good.The method can be fiber cloth reinforced severe Damage the related design of Component in Single Rectangular Section armored concrete ultimate load and scientific research provides prediction, to reduce test Actual measurement group number, save actual measurement expense and lot of experiments time, so that strenthening member ultimate bearing capacity is designed more accurate；To reinforcing The Ultimate Bearing Capacity of beam is accurately calculated, and makes engineers and technicians' fiber cloth reinforced beam of more accurate and convenient control Loading procedure；Calculating process is easy, and suitable ordinary skill technical staff uses, and has larger economic benefit.

Brief description

Fig. 1 is Ultimate Strength sketch-cross section

Fig. 2 is Ultimate Strength sketch-strain distribution on sections

Fig. 3 is Ultimate Strength sketch-stress distribution

Fig. 4 is the b01-yl-1b beam crack area l of the embodiment of the present invention₁、l₂And l₃Measure schematic diagram

Specific embodiment

With reference to embodiment and referring to the drawings the invention will be further described.

A kind of Ultimate Bearing Capacity computational methods of fiber cloth reinforced severe injury beam, comprise the steps:

The geometrical relationship that s1 is strained by section of beam, the strain-stress relation of material, set up mechanical model, calculate phase To depth of compressive zone

${\mathrm{\&xi;}}_n=\frac{-b+\sqrt{b^2-4ac}}{2a}$

In formula, a, b, c are coefficient, are expressed as follows respectively:

A=0.798f_cbh₀ ², b=0.0033e_ba_bh-f_ya_sh₀, c=-0.0033e_ba_bH, wherein, f_cAxle for concrete Heart comprcssive strength, a_sFor the total cross-section area of tension reinforcement, a_bFor the total cross-section area of different numbers of plies bfrp, h₀For section Effective depth, h be beam section height, f_yFor the yield strength of reinforcing bar, e_bElastic modelling quantity for bfrp；

After calculating a, b and c, bring above-mentioned formula into and can calculate depth of compressive zone；

S2 carries out reduction to compressive region concrete axial compressive strength；

S3 adopts the concrete axial compressive strength after reduction, recalculates depth of compressive zone by above-mentioned steps；

S4 calculating limit moment of flexure；

S5 calculating limit anti-bending bearing capacity.

The present invention is when carrying out depth of compressive zone calculating, specific as follows:

It is believed that the reinforced beam of poisoning injury meets plane section Jiading after reinforcing in calculating process；Reinforcing bar Strain-stress relation is two-part, and after reinforcement yielding, tensile strength takes yield value；The stress-strain of bfrp linearly closes System；Two-part is adopted, the mathematic(al) representation of its strain-stress relation is as follows during concrete axial compression:

${\mathrm{\&sigma;}}_c=\left\{\begin{array}{cc}{f}_c\&lsqb;1-{(1-\frac{{\mathrm{\&epsiv;}}_c^t}{{\mathrm{\&epsiv;}}_0})}^2\&rsqb;& {\mathrm{\&epsiv;}}_c\&le;{\mathrm{\&epsiv;}}_0\\ f_c& {\mathrm{\&epsiv;}}_0<{\mathrm{\&epsiv;}}_c\&le;{\mathrm{\&epsiv;}}_{cu}\end{array}\right.---\left(1\right)$

In formula, σ_cFor compressive strain ε_cThe stress of corresponding concrete；f_cAxial compressive strength for concrete；It is subject to for beam The compressive strain of nip edge concrete；ε₀Reach f for compressive stress_cWhen concrete compressive strain；ε_cuLimit pressure for concrete should Become；When the cubic compressive strength of concrete is not higher than c50, ε₀It is taken as 0.002, ε_cuIt is taken as 0.0033；

Reinforced beam for severe injury post-reinforcing does not consider that when calculating concrete in tension zone acts on.Section Calculation diagram, as Figure 1-3.Due to bfrp cloth and bondline thickness compared with deck-molding very little it is believed that its cross section shape The application point b of the heart is located at the lower edge of beam, sets up geometrical relationship according to Fig. 2 as follows:

$\frac{1}{\mathrm{\&rho;}}=\frac{{\mathrm{\&epsiv;}}_c^t}{{\mathrm{\&xi;}}_n{h}_0}=\frac{{\mathrm{\&epsiv;}}_s}{(1-{\mathrm{\&xi;}}_n)h_0}=\frac{{\mathrm{\&epsiv;}}_c}{y}=\frac{{\mathrm{\&epsiv;}}_{tb}}{(1-{\mathrm{\&xi;}}_n)h}---\left(2\right)$

In formula, the radius of curvature that ρ reaches capacity during bearing capacity for beams of concrete；Pressure for beam pressurized area edge concrete Strain；ξ_nFor the ratio of concrete compression area height and effective depth of section, i.e. relative height of compression zone；h₀Effective for section Highly；ε_sThe tensile stress sigma of reinforcing bar_sCorresponding strain；ε_cAway from natural axis distance for y at fiber strain；ε_tbFor bfrp cloth tension σ_tbCorresponding strain；H is beam section height；

Severe injury reinforced beam after reinforcing, compressive region concrete be in elastic-plastic phase it is believed thatMeetSevere injury reinforced beam reinforcing bar before reinforcing has been surrendered, and after reinforcing, reinforcing bar is still in yield situation； Bfrp stress-strain during tension linearly changes, and the physical relation obtaining each material in conjunction with above formula (2) is as follows:

${\mathrm{\&sigma;}}_c=f_c,{\mathrm{\&sigma;}}_s=f_y,{\mathrm{\&sigma;}}_{tb}=e_b{\mathrm{\&epsiv;}}_{tb}=e_b\frac{1-{\mathrm{\&xi;}}_n}{{\mathrm{\&xi;}}_n{h}_0}{\mathrm{\&epsiv;}}_c^{t}h---\left(3\right)$

In formula, f_yYield strength for reinforcing bar；e_bElastic modelling quantity for bfrp；

The strain-stress relation formula during concrete compression shown in formula (1) and the geometry shown in formula (2) is applied to close System, according to the calculation diagram of Fig. 3, tries to achieve the pressure f of compressive region concrete respectively by integral operation_cAnd its application point is to pressurized Area concrete edge apart from y_c, as follows:

$f_c=f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})---\left(4\right)$

$y_c={\mathrm{\&xi;}}_n{h}_0\&lsqb;1-\frac{\frac{1}{2}-\frac{1}{12}{\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_c^t}\right)}^2}{1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t}}\&rsqb;---\left(5\right)$

According to the stress distribution of Fig. 3, axially set up the equation of static equilibrium: ∑ f along beam_x=0, obtain

$f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})-f_y{a}_s-e_b\frac{1-{\mathrm{\&xi;}}_n}{{\mathrm{\&xi;}}_n{h}_0}{\mathrm{\&epsiv;}}_c^t{\mathrm{ha}}_b=0---\left(6\right)$

In formula, a_sTotal cross-section area for tension reinforcement；a_bTotal cross-section area for different numbers of plies bfrp；By public affairs Formula (6) solves and draws ξ_n；

WhenWhen, compressive region concrete is crushed, and section is destroyed, and beam loses bending bearing capacity, to comprcssive strength Grade is not more than the concrete of c50, takesε₀=0.002, and substitute into formula (6), collated

aξ_n ²+bξ_n+ c=0 (7)

Then solution quadratic equation with one unknown can obtain

${\mathrm{\&xi;}}_n=\frac{-b+\sqrt{b^2-4ac}}{2a}---\left(8\right)$

In formula, a, b and c are coefficient, are expressed as follows respectively:

A=0.798f_cbh₀ ², b=0.0033e_ba_bh-f_ya_sh₀, c=-0.0033e_ba_bh (9)

After calculating a, b and c, bring formula (7) into, you can calculate ξ_n；

Then depth of compressive zone x_nFor

x_n=ξ_nh₀(10)

In the present invention, because severe injury reinforced beam may extended to compressive region height by curved rear span centre crack In the range of degree, and the presence in crack will necessarily weaken the comprcssive strength of depth of compressive zone inner concrete, then this part concrete Comprcssive strength is accomplished by carrying out reduction when calculating.Strength reduction method is as follows:

S2.1 damage before reinforcing crackle does not occur in the range of reinforced beam depth of compressive zone when, concrete anti- Compressive Strength takes former strength grade of concrete corresponding axial compressive strength standard value, that is,

f_c=f_ck(11)

When s2.2 is in the range of cracks can spread before reinforcing to damage reinforced beam depth of compressive zone, the resistance to compression of concrete Intensity level is calculated as follows:

f_c=η f_ck(12)

In formula,For the compressive strength decreasing coefficient of damaged concrete, wherein,It is by curved Area 3 crack top to beam top edge minimum range meansigma methodss, l₁、l₂And l₃It is to beam top edge by curved area 3 crack top Minimum range.

Taking the b01-yl-1b beam crack area before reinforcing as a example, determine l₁、l₂And l₃Value, as shown in figure 4, can by measurement With obtain l₁=34.94mm, l₂=41.31mm, l₃=47.28mm.The meaning of the method is former for compressive region intact coagulation The comprcssive strength of soil is shared out equally in the range of the depth of compressive zone damaging reinforced beam, so being capable of science and easily Reflection damages the true anti-pressure ability of back rest depth of compressive zone scope inner concrete.

In the present invention, due to the impaired reinforced beam of severe after reinforcing, mostly bfrp is intact, and reinforcing bar is bent Destroy in the case that clothes are crushed with compressive region, now the anti-bending bearing capacity of beam depends primarily on the anti-of compressive region concrete Compressive Strength and the yield strength of tension reinforcement, the increase of the fiber cloth number of plies can make the depth of compressive zone of beam increase, and then to beam Bearing capacity produces impact, but during beam loses bearing capacity, fiber cloth is destroyed, and tensile strength meets requirement, because This does not need the intensity index of fiber cloth is any limitation as.During calculating limit moment of flexure, specifically comprise the following steps that

According to the stress distribution of Fig. 3, torque equilibrium equation: ∑ m is built with fiber cloth application point b_b=0, obtain

$m=f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})\{h-{\mathrm{\&xi;}}_n{h}_0\&lsqb;1-\frac{\frac{1}{2}-\frac{1}{12}{\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_c^t}\right)}^2}{1-\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_c^t}}\&rsqb;\}-f_y{a}_s{a}_s---\left(13\right)$

In formula: a_sThe vertical dimension away from the tension reinforcement cross section centre of form for the fiber cloth；

WhenWhen, compressive region concrete is crushed, and section is destroyed, and beam loses bending bearing capacity；To comprcssive strength Grade is not more than the concrete of c50, takesε₀=0.002, and substitute into formula (13), collated

M=0.798f_cbξ_nh₀(h-0.412ξ_nh₀)-f_ya_sa_s(14)

In formula, ξ_nFor relative height of compression zone f_cAxial compressive strength for concrete；H is beam section height；h₀For section Effective depth；a_sTotal cross-section area for tension reinforcement；f_yYield strength for reinforcing bar；a_sFiber cloth is horizontal away from tension reinforcement The vertical dimension of cross-section centroid.

In the present invention, during calculating limit anti-bending bearing capacity, for three branch load modes, the limit lotus of reinforced beam Load following formula represents:

$p_u=\frac{6m}{l_0}---\left(15\right)$

In formula: l₀Clear span for beam.

It is below the specific embodiment using technical scheme disclosed by the invention:

Now computing formula is used taking b0-yl-1 beam as a example.Severe injury reinforced beam concrete strength etc. Level c40, average cubic compressive strength is 42.8mpa, according to specification, takes f_ck=26.8mpa, b=200mm, h=300mm, h₀ =269mm, e_b=105gpa, a_b=1 × 190mm × 0.115mm=21.85mm², f_y=426.7mpa, a_s=340mm², a_s= 31mm, l₀=2.1m.Concrete calculating process is as follows:

(1) above-mentioned parameter is brought into formula (9) and calculate a, b and c value, obtain a=309508258.1n mm, b=- 36639892.2n mm, c=-2271307.5n mm.

A, b and c value is brought into formula (8), calculates ξ_n=0.1633, then depth of compressive zone x_n=ξ_nh₀=43.93mm.

(2) according to Fig. 4, reinforce front crack and have been extended in the range of depth of compressive zone, concrete crushing strength needs Carry out reduction by formula (12).ThenConcrete crushing strength is rolled over Subtract coefficientConcrete axial compressive strength f_c=0.937 × 26.8mpa=25.11mpa.

(3) adopt the concrete crushing strength f after reduction_c=25.11mpa, recalculates ξ by above-mentioned steps_n, obtain ξ_n= 0.1719.

(4) by above-mentioned parameter and result of calculation, bring formula (14) into, obtain m=47.58kn m.

(5) according to formula (15), calculating limit load, obtain p_u=135.95kn.

Following table provides result of calculation example.

The calculating process of other two groups of beams is similar with said process, repeats no more.The severe injury steel reinforced using bfrp The comparing result of the Ultimate Bearing Capacity test value of Concrete Beam Reinforced and value of calculation is as shown in table 1.

Table 1 Ultimate Bearing Capacity test value and value of calculation

The limit that the present invention passes through to arrange 2 groups of Test and Comparison Study external application bfrp reinforcing severe injury reinforced beams resists Curved bearing capacity, analysis bfrp reinforces damage -form, bearing capacity, load-deflection curves and the fibre of severe injury reinforced beam Dimension cloth load-deflection curves etc., establish the limit bending resistance that a kind of basalt fiber cloth reinforces severe injury reinforced beam Bearing capacity formula, calculates a kind of new approach of offer for solving reinforced beam reinforcing after suffering from major injury, And passing through verification experimental verification, value of calculation and result of the test are coincide good.

The above is only the preferred embodiment of the present invention, is not intended to limit；Although it should be pointed out that with reference to above-mentioned each Embodiment has been described in detail to the present invention, it will be understood by those within the art that, it still can be to above-mentioned each Technical scheme described in embodiment is modified, or carries out equivalent to wherein some or all of technical characteristic；And this A little scopes changed and replace, do not make the essence disengaging various embodiments of the present invention technical scheme of corresponding technical scheme.

Claims (5)

1. a kind of Ultimate Bearing Capacity computational methods of fiber cloth reinforced severe injury beam are it is characterised in that include following walking Rapid:

The geometrical relationship that s1 is strained by section of beam, the strain-stress relation of material, set up mechanical model, calculate and be relatively subject to Nip height

${\mathrm{\&xi;}}_n=\frac{-b+\sqrt{b^2-4ac}}{2a}$

In formula, a, b, c are coefficient, are expressed as follows respectively:

A=0.798f_cbh₀ ², b=0.0033e_ba_bh-f_ya_sh₀, c=-0.0033e_ba_bH, wherein, f_cAxle center for concrete resists Compressive Strength, a_sFor the total cross-section area of tension reinforcement, a_bFor the total cross-section area of different numbers of plies bfrp, h₀Having for section Effect height, h is beam section height, f_yFor the yield strength of reinforcing bar, e_bElastic modelling quantity for bfrp；

After calculating a, b and c, bring above-mentioned formula into and can calculate depth of compressive zone；

S2 carries out reduction to compressive region concrete axial compressive strength；

S3 adopts the concrete axial compressive strength after reduction, recalculates depth of compressive zone by above-mentioned steps；

S4 calculating limit moment of flexure；

S5 calculating limit anti-bending bearing capacity.

2. the Ultimate Bearing Capacity computational methods of a kind of fiber cloth reinforced severe injury beam according to claim 1, its It is characterised by, when carrying out depth of compressive zone calculating, specific as follows:

It is believed that the reinforced beam of poisoning injury meets plane section Jiading after reinforcing in calculating process；The stress of reinforcing bar- Strain stress relation is two-part, and after reinforcement yielding, tensile strength takes yield value；The stress-strain of bfrp is linear；Coagulation Two-part is adopted, the mathematic(al) representation of its strain-stress relation is as follows during native axial compression:

${\mathrm{\&sigma;}}_c=\left\{\begin{array}{cc}{f}_c\&lsqb;1-{(1-\frac{{\mathrm{\&epsiv;}}_c^t}{{\mathrm{\&epsiv;}}_0})}^2\&rsqb;& {\mathrm{\&epsiv;}}_c\&le;{\mathrm{\&epsiv;}}_0\\ f_c& {\mathrm{\&epsiv;}}_0<{\mathrm{\&epsiv;}}_c\&le;{\mathrm{\&epsiv;}}_{cu}\end{array}\right.---\left(1\right)$

In formula, σ_cFor compressive strain ε_cThe stress of corresponding concrete；f_cAxial compressive strength for concrete；For beam compressive region side The compressive strain of edge concrete；ε₀Reach f for compressive stress_cWhen concrete compressive strain；ε_cuCompressive ultimate strain for concrete；When mixed When the cubic compressive strength of solidifying soil is not higher than c50, ε₀It is taken as 0.002, ε_cuIt is taken as 0.0033；

Reinforced beam for severe injury post-reinforcing does not consider that when calculating concrete in tension zone acts on, due to bfrp cloth And bondline thickness compared with deck-molding very little it is believed that its cross section centre of form application point be located at beam lower edge, set up set Relation is as follows:

$\frac{1}{\mathrm{\&rho;}}=\frac{{\mathrm{\&epsiv;}}_c^t}{{\mathrm{\&xi;}}_n{h}_0}=\frac{{\mathrm{\&epsiv;}}_s}{(1-{\mathrm{\&xi;}}_n)h_0}=\frac{{\mathrm{\&epsiv;}}_c}{y}=\frac{{\mathrm{\&epsiv;}}_{tb}}{(1-{\mathrm{\&xi;}}_n)h}---\left(2\right)$

In formula, the radius of curvature that ρ reaches capacity during bearing capacity for beams of concrete；Compressive strain for beam pressurized area edge concrete； ξ_nFor the ratio of concrete compression area height and effective depth of section, i.e. relative height of compression zone；h₀Effective depth for section； ε_sThe tensile stress sigma of reinforcing bar_sCorresponding strain；ε_cAway from natural axis distance for y at fiber strain；ε_tbFor bfrp cloth tensile stress sigma_tbRight The strain answered；H is beam section height；

Severe injury reinforced beam after reinforcing, compressive region concrete be in elastic-plastic phase it is believed thatMeetSevere injury reinforced beam reinforcing bar before reinforcing has been surrendered, and after reinforcing, reinforcing bar is still in yield situation； Bfrp stress-strain during tension linearly changes, and the physical relation obtaining each material in conjunction with above formula is as follows:

${\mathrm{\&sigma;}}_c=f_c,{\mathrm{\&sigma;}}_s=f_y,{\mathrm{\&sigma;}}_{tb}=e_b{\mathrm{\&epsiv;}}_{tb}=e_b\frac{1-{\mathrm{\&xi;}}_n}{{\mathrm{\&xi;}}_n{h}_0}{\mathrm{\&epsiv;}}_c^{t}h---\left(3\right)$

In formula, f_yYield strength for reinforcing bar；e_bElastic modelling quantity for bfrp；

Apply the strain-stress relation formula during concrete compression shown in formula (1) and the geometrical relationship shown in formula (2), lead to Cross the pressure f that compressive region concrete is tried to achieve in integral operation respectively_cAnd its application point to compressive region concrete edge apart from y_c, such as Shown in lower:

$f_c=f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})---\left(4\right)$

$y_c={\mathrm{\&xi;}}_n{h}_0\&lsqb;1-\frac{\frac{1}{2}-\frac{1}{12}{\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_c^t}\right)}^2}{1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t}}\&rsqb;---\left(5\right)$

According to stress distribution, axially set up the equation of static equilibrium: ∑ f along beam_x=0, obtain

$f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})-f_y{a}_s-e_b\frac{1-{\mathrm{\&xi;}}_n}{{\mathrm{\&xi;}}_n{h}_0}{\mathrm{\&epsiv;}}_c^t{\mathrm{ha}}_b=0---\left(6\right)$

In formula, a_sTotal cross-section area for tension reinforcement；a_bTotal cross-section area for different numbers of plies bfrp；By formula (6) Solution draws ξ_n；

WhenWhen, compressive region concrete is crushed, and section is destroyed, and beam loses bending bearing capacity, to grade of compressive strength It is not more than the concrete of c50, takeε₀=0.002, and substitute into formula (6), collated

aξ_n ²+bξ_n+ c=0 (7)

Then solution quadratic equation with one unknown can obtain

${\mathrm{\&xi;}}_n=\frac{-b+\sqrt{b^2-4ac}}{2a}---\left(8\right)$

In formula, a, b and c are coefficient, are expressed as follows respectively:

A=0.798f_cbh₀ ², b=0.0033e_ba_bh-f_ya_sh₀, c=-0.0033e_ba_bh (9)

After calculating a, b and c, bring formula (7) into, you can calculate ξ_n；

Then depth of compressive zone x_nFor

x_n=ξ_nh₀(10).

3. the Ultimate Bearing Capacity computational methods of a kind of fiber cloth reinforced severe injury beam according to claim 2, its It is characterised by, when reduction is carried out to compressive region concrete axial compressive strength, specifically comprise the following steps that

When crackle in the range of damage reinforced beam depth of compressive zone before reinforcing in s2.1, the pressure resistance of concrete Degree takes former strength grade of concrete corresponding axial compressive strength standard value, that is,

f_c=f_ck(11)

When s2.2 is in the range of cracks can spread before reinforcing to damage reinforced beam depth of compressive zone, the comprcssive strength of concrete Value is calculated as follows:

f_c=η f_ck(12)

In formula,For the compressive strength decreasing coefficient of damaged concrete, wherein,It is by 3, curved area Crack tip to beam top edge minimum range meansigma methodss, l₁、l₂And l₃It is by curved area 3 crack top to beam top edge Small distance.

4. the Ultimate Bearing Capacity computational methods of a kind of fiber cloth reinforced severe injury beam according to claim 3, its It is characterised by, during calculating limit moment of flexure, specifically comprise the following steps that

According to stress distribution, torque equilibrium equation: ∑ m is built with fiber cloth application point_b=0, obtain

$m=f_c{\mathrm{b\&xi;}}_n{h}_0(1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t})\{h-{\mathrm{\&xi;}}_n{h}_0\&lsqb;1-\frac{\frac{1}{2}-\frac{1}{12}{\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_c^t}\right)}^2}{1-\frac{{\mathrm{\&epsiv;}}_0}{3{\mathrm{\&epsiv;}}_c^t}}\&rsqb;\}-f_y{a}_s{a}_s---\left(13\right)$

In formula: a_sThe vertical dimension away from the tension reinforcement cross section centre of form for the fiber cloth；

WhenWhen, compressive region concrete is crushed, and section is destroyed, and beam loses bending bearing capacity；To grade of compressive strength It is not more than the concrete of c50, takeε₀=0.002, and substitute into formula (13), collated

M=0.798f_cbξ_nh₀(h-0.412ξ_nh₀)-f_ya_sa_s(14)

In formula, ξ_nFor relative height of compression zone f_cAxial compressive strength for concrete；H is beam section height；h₀Having for section Effect height；a_sTotal cross-section area for tension reinforcement；f_yYield strength for reinforcing bar；a_sFiber cloth is away from tension reinforcement cross section The vertical dimension of the centre of form.

5. the Ultimate Bearing Capacity computational methods of a kind of fiber cloth reinforced severe injury beam according to claim 4, its It is characterised by, during calculating limit anti-bending bearing capacity, for three branch load modes, the ultimate load following formula of reinforced beam Represent:

$p_u=\frac{6m}{l_0}---\left(15\right)$

In formula: l₀Clear span for beam.