CN101936852A - Confirming method of axial compression bearing capacity of steel tube-FRP (Fiber Reinforced Plastic)-concrete column as well as application - Google Patents

Confirming method of axial compression bearing capacity of steel tube-FRP (Fiber Reinforced Plastic)-concrete column as well as application Download PDF

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CN101936852A
CN101936852A CN 201010225646 CN201010225646A CN101936852A CN 101936852 A CN101936852 A CN 101936852A CN 201010225646 CN201010225646 CN 201010225646 CN 201010225646 A CN201010225646 A CN 201010225646A CN 101936852 A CN101936852 A CN 101936852A
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steel pipe
concrete column
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CN101936852B (en
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查晓雄
仓友清
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Shenzhen Graduate School Harbin Institute of Technology
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Abstract

The invention relates to a confirming method of the axial compression bearing capacity of a steel tube-FRP (Fiber Reinforced Plastic)-concrete column. In the steel tube-FRP-concrete column, an FRP tube is arranged between a steel tube and concrete of a concrete-filled steel tubular column. The confirming method of the axial compression bearing capacity of the steel tube-FRP)-concrete column comprises the following steps of: step (100): collecting related parameters including the yield strength of steel in the steel tube-FRP-concrete, the circumferential tensile strength of a FRP tubular product, the axis compressive strength of the concrete, and collecting the parameters of the cross section areas of the steel tube, the FRP tube and the concrete in the concrete-filled steel tube; and confirming the axial compression bearing capacity that Nu=fscAsc, wherein Nu presents the axial compression bearing capacity, fsc and Asc are presented by the equations in the specification, xi 1 is the confining factor of the steel tube and the FRP tube and satisfies an equation: xi 1=(Asfv+0.5Affh)/Acfck, As, Af and Ac respectively present the cross section areas of the steel tube, the FRP tube and the concrete, fy, fh and fck are respectively the yield strength of the steel, the circumferential tensile strength of the FRP tubular product and the axis compressive strength of the concrete, and fsc and Asc are respectively the axial compressive strength and the cross section area of a component. The confirming method of the axial compression bearing capacity of the steel tube-FRP-concrete column acquires the corrected confining factor of the steel tube-FRP-concrete by adopting a steel tube-FRP-concrete model through correcting the confining factor of the concrete-filled steel tubular column and can accurately confirm the axial compression bearing capacity of the steel tube-FRP-concrete column.

Description

A kind of steel pipe-FRP-concrete column capacity under axial is determined method and application
Technical field
The present invention relates to a kind of concrete column capacity under axial and determine method and application, relate in particular to a kind of steel pipe-FRP-concrete column capacity under axial and determine method and application.
Background technology
Along with the development of Building technology, concrete filled steel tube is more and more to be applied in the building element, as the pillar of skyscraper, bridge pier, tower bar, stake etc.Steel core concrete column plays main load-bearing effect in these building elements, therefore, determine that scientifically the intensity of concrete filled steel tube combined material is very important in real world applications.In the prior art, in order to make steel pipe corrosion-resistant, adopt between the steel pipe of steel core concrete column and concrete FPR (Fiber Reinforced Plastics, fibre-reinforced plastics are set, be called for short " FRP ") manage, so just improved the corrosion resistance of steel core concrete column.In the prior art, do not have the convenient method that is suitable for to calculate, influenced the steel pipe-practicality of FRP-concrete column in engineering greatly for steel pipe-FRP-concrete column capacity under axial.
Summary of the invention
The technical matters that the present invention solves is: provide a kind of steel pipe-FRP-concrete column capacity under axial to determine method, overcoming in the prior art does not have the convenient method that is suitable for to calculate for steel pipe-FRP-concrete column capacity under axial, has influenced the technical matters of the steel pipe-practicality of FRP-concrete column in engineering greatly.
Technical scheme of the present invention is: provide a kind of steel pipe-FRP-concrete column capacity under axial to determine method, described steel pipe-FRP-concrete column is that the FPR pipe is set between the steel pipe of steel core concrete column and concrete, and steel pipe-FRP-concrete column capacity under axial determines that method comprises the steps:
Step 100: gather correlation parameter: gather the yield strength of steel in steel pipe-FRP-concrete, the hoop tensile strength and the concrete axial compressive strength of FRP pipe, gather steel pipe in the concrete filled steel tube, FRP pipe and concrete cross-sectional area.
Determine capacity under axial: N u=f ScA Sc, wherein: N uThe expression capacity under axial,
Figure BSA00000188401300021
A Sc=A s+ A c+ A f, in the formula, ξ 1Cuff coefficient for steel pipe and FRP pipe satisfies ξ 1=(A sf y+ 0.5A ff h)/A cf c, A s, A f, A cBe respectively steel pipe, FRP pipe and concrete cross-sectional area; f y, f hAnd f CkBe respectively the yield strength of steel, the hoop tensile strength and the concrete axial compressive strength of FRP pipe.f Sc, A ScBe respectively the combination axial compressive strength and the cross-sectional area of member.
Further technical scheme of the present invention is: in definite capacity under axial step, be included on the basis of steel core concrete column the cuff coefficient is revised to be suitable for steel pipe-FRP-concrete column.
Further technical scheme of the present invention is: in definite capacity under axial step, comprise that structure steel pipe-FRP-concrete column model is to obtain on the basis of steel core concrete column the correction to the cuff coefficient.
Further technical scheme of the present invention is: in definite capacity under axial step, making up steel pipe-FRP-concrete column model is the correction to skeleton curve restoring force model.
Further technical scheme of the present invention is: in definite capacity under axial step, comprise steel pipe-FRP-concrete column displacement ductility is derived.
Technical scheme of the present invention is: steel pipe-FRP-concrete column capacity under axial determines that method is applied to steel pipe-FRP-concrete column.
Technique effect of the present invention is: steel pipe of the present invention-FRP-concrete column capacity under axial determines that method passes through the correction to steel core concrete column cuff coefficient, adopts steel pipe-FRP-concrete model to obtain the concrete cuff coefficient of revised steel pipe-FRP-.Steel pipe of the present invention-FRP-concrete column capacity under axial determines that method can accurately determine steel pipe-FRP-concrete column capacity under axial.
Description of drawings
Fig. 1 is a process flow diagram of the present invention.
Fig. 2 is a lamina off-axis stretching synoptic diagram of the present invention.
Fig. 3 is a P-△ skeleton curve eighty percent discount line computation model of the present invention.
Fig. 4 is a P-△ skeleton curve tri linear computation model of the present invention.
Embodiment
Below in conjunction with specific embodiment, technical solution of the present invention is further specified.
As shown in Figure 1, the specific embodiment of the present invention is: provide a kind of steel pipe-FRP-concrete column capacity under axial to determine method, described steel pipe-FRP-concrete column is that the FPR pipe is set between the steel pipe of steel core concrete column and concrete, and steel pipe-FRP-concrete column capacity under axial determines that method comprises the steps:
Step 100: gather correlation parameter, that is, gather the yield strength of steel in steel pipe-FRP-concrete, the hoop tensile strength and the concrete axial compressive strength of FRP tubing, gather steel pipe in the concrete filled steel tube, FRP pipe and concrete cross-sectional area.
Step 200: determine capacity under axial: N u=f ScA Sc, wherein: N uThe expression capacity under axial, A Sc=A s+ A c+ A f, ξ 1Cuff coefficient for steel pipe and FRP pipe satisfies ξ 1=(A sf y+ 0.5A ff h)/A cf c, A s, A f, A cBe respectively steel pipe, FRP pipe and concrete cross-sectional area; f y, f hAnd f CkBe respectively the yield strength of steel, the hoop tensile strength and the concrete axial compressive strength of FRP pipe.f Sc, A ScBe respectively the combination axial compressive strength and the cross-sectional area of member.
Detailed process is as follows:
One, concrete filled steel tube combined strength.
Yu Min etc. revise hollow, the filled polygon concrete filled steel tube unified strength theory of the kind paulownia of clock, and the combined strength computing formula that has obtained concrete filled steel tube is:
f sc＝(1+η)[(1-β)f ck+βf y] (1)
η represents the cuff reinforcing coefficient in the formula, has
Figure BSA00000188401300041
β represents the steely ratio, equals the steel area A sWith the concrete filled steel tube area A ScRatio,
Figure BSA00000188401300042
With the pass of steel ratio α be β=α/(1+ α);
Ω represents solid rate, has
Figure BSA00000188401300043
With the pass of hollow rate be Ω=1-ψ;
ξ ScRepresent solid cuff coefficient, ξ is arranged for the solid steel pipe concrete Sc=ξ s
By recurrence, determine that finally value is A=2.0, B=0.05, C=0.2, D=-0.05 to existing concrete filled steel tube axial compression short column.Simplify processing based on following formula.The cuff coefficient of getting member is ξ=A sf y/ A cf Ck, steel are got Q235 to Q420 in common engineering, and concrete is from C30 to C80, and 0.2 α=0.008～0.04 then has:
1 2 + 0.2 α ( 1 - ψ ) + 0.05 α f y f ck ψ ≈ 0.5 - - - ( 2 )
Concrete filled steel tube is unified the simplification computing formula of intensity and is seen (3-3)
f sc = 1 + 1.5 ξ 1 + A s / A c f ck - - - ( 3 )
Wherein: ξ=A sf y/ A cf Ck
Two, steel pipe-FRP pipe-concrete column capacity under axial.
The cuff effect of steel pipe-FRP pipe-concrete column is made up of steel pipe and FRP pipe two parts.Because the FRP tubular axis is less to rigidity, ignores the FRP tubular axis to stressed contribution to the whole member bearing capacity at this.According to general theory thought, the cuff power that FRP manages and steel pipe provides is carried out equivalence, the cuff coefficient of the unitized construction that the present invention proposes is
ξ 1 = ξ s + ξ f = A s f y A c f c + k A f f h A c f c - - - ( 4 )
Because the cuff effect of FRP is mainly reflected in strain, and this moment, steel pipe reached surrender.Introduce the reduction coefficient that k is the effect of FRP cuff herein.Result according to this paper finite element analogy gets k=0.5.Then the concrete combined strength of steel pipe-FRP-that obtains based on concrete filled steel tube general theory formula of reduction is:
f sc = 1 + 1.5 ξ 1 1 + A s / A c f ck - - - ( 5 )
The capacity under axial of member:
N u＝f scA sc (6)
Wherein: ξ 1Formula (4), A are seen in calculating Sc=A s+ A c+ A fξ 1Cuff coefficient for steel pipe and FRP pipe satisfies ξ 1=(A sf y+ 0.5A ff h)/A cf c, A s, A f, A cBe respectively steel pipe, FRP pipe and concrete cross-sectional area; f y, f hAnd f CkBe respectively the yield strength of steel, the hoop tensile strength and the concrete axial compressive strength of FRP pipe.f Sc, A ScBe respectively the combination axial compressive strength and the combined area of member.
f hBe the hoop tensile strength of FRP pipe, can draw test method (ASTM D 2290-04) to carry out according to the FRP pipe ring.For twining the ring specimen that FRP manages the hoop tension test of intercepting, get f from intersecting h=1.75f H, FRP, all the other methods (laminate Theoretical Calculation, treadmill test or manufacturer's data etc.) are got f h=f H, FRP
As do not have test parameters, can adopt Classical lamination theory to derive.Fig. 2 is the lamina off-axis stressed synoptic diagram that stretches, and x wherein, y represent the hoop of FRP pipe and axially respectively, and 1 and 2 are respectively along machine direction with perpendicular to machine direction.θ be machine direction and tubular axis to angle.By coordinate transform, obtain the components of stress of material major axes orientation.
σ 1＝σ hsin 2θ (7)
σ 2＝σ hcos 2θ (8)
τ 12＝-σ hsinθcosθ (9)
When θ when 0 ~ 90 ° changes, σ 1And σ 2All be on the occasion of, this moment, the Tsai-Hill criterion was
( σ 1 X t ) 2 + ( σ 2 Y t ) 2 + ( τ 12 S 12 ) 2 - ( σ 1 X t ) ( σ 2 X t ) = 1 - - - ( 10 )
In the formula: X tBe expressed as the tensile strength of the machine direction of lamina, Y tThe tensile strength of expression resin direction, S 12Shear resistance in the presentation surface.
With components of stress σ 1, σ 2, τ 12With intensity index X t, Y t, S 12Substitution is also put in order, can obtain the computing formula of hoop ultimate stress under the different winding angles:
σ h = 1 sin 4 θ X t 2 + cos 4 θ Y t 2 + sin 2 θ cos 2 θ S 12 2 - cos 2 θ sin 2 θ X t 2 - - - ( 11 )
When fiber all when hoop twines, θ=90 °, σ h=X t
When the FRP pipe was symmetrical laminated plate structure, employing formula (11) prediction loop was to the hoop tensile strength of FRP pipe.
Three, the correction of the simplified model of skeleton curve.
Zhong Shantong etc. have proposed to be adapted to concrete filled steel tube bending component P-△ hysteresis loop and skeleton curve model according to a large amount of tests and finite element analysis, and two kinds on two segmented line models and tri linear model arranged.Be used for simulating no descending branch and the skeleton curve that descending branch is arranged respectively.Two segmented line models are seen Fig. 3, and the tri linear model is seen figure four.Zhang Fengliang returns by theoretical analysis and finite element based on the skeleton curve model of existing solid steel pipe concrete, has obtained the restoring force model of suitable concrete-filled steel tubular hollow.
The present invention revises existing skeleton curve restoring force model, has obtained being fit to the simplified model of steel pipe of the present invention-FRP pipe-concrete component.
As shown in Figure 3, for two segmented line models, have three parameters, i.e. the stiffness K of elastic stage a, yield load P yStiffness K with strain bFor the tri linear model, have four parameters, be respectively the stiffness K of elastic stage a, ultimate load P u, descending branch starting point place displacement δ pStiffness K with descending branch t
Parameter definite as follows:
K a＝3E scI sc/L 3 (12)
E in the formula ScI ScBe the combination bendind rigidity of member, E ScI Sc=E sI s+ E fI f+ 0.6E cI c, E f, I fBe respectively axial modulus of elasticity and the moment of inertia of FRP.Because the elastic modulus of FRP is compared little a lot with steel, also this can be ignored in the computation process.Formula 12 is applicable to two kinds of models simultaneously.
P y = ( - 0.97 n 2 - 0.564 n + 1.671 ) × ( 0.253 × ξ + 1.602 ) 1.368 × λ / 20 + 1.534 × M y / L - - - ( 13 )
Formula (13) is the computing formula of ultimate load (yield load).Because in the present invention, cuff power is provided jointly by steel pipe and FRP pipe, and the cuff coefficient is revised, and ξ=ξ is arranged s+ k ξ f=(A sf y+ 0.5A ff h)/A cf cM in the formula yBe yield moment, be defined as the moment of flexure value at intersection point place of the extended line of the extended line of elastic stage and strain, M is arranged y=0.89 γ mM 0', γ mFor considering the development coefficient of plasticity.
Formula (14) is the letdown point place formula for calculating displacement that Zhang Fengliang proposes in " research of open circles concrete filled steel tubular compression bending member skeleton curve and ductility factor ".The cuff coefficient is revised, ξ=ξ is arranged s+ k ξ f=A sf y+ 0.5A ff h/ A cf c, K aAnd P yGet revised value.
δ p＝(0.5n 2-0.98n-0.901)×(0.071ξ-0.953)×(0.097λ/20+1.727)×P y/K a (14)
When calculating descending branch rigidity, inlet coefficient α b=K t/ K a, α in the Zhong Shantong work " concrete filled steel tube " bCalculating see formula (15).
K t = [ 1.151 ( 0.018 + 0.026 n 1 - 0.012 n 1 2 ) - 0.104 n 1 λ 2 f ck ( 1 - α ) + α f y E s - ( E s - E c ) ( 1 - α ) 2 ] K a - - - ( 15 )
Because the brittle rupture of FRP can make bearing of component reduce, make the descending branch slope become big.In order to consider of the influence of this factor, the axial compression ratio n in the formula is revised the restoring force model.Be n 1=β n, n are the axial compression ratio of member, the axial compression ratio enhancement coefficient of β for considering that FRP destroys, β=f Sc/ f Sc0, f ScBe the yield strength of combined member, f Sc 0The yield strength that does not contain the FRP pipe component for correspondence.Consider that again the unstable failure of member takes place prior to material damage, is thought of as the stability factor when member when slenderness ratio is big
Figure BSA00000188401300081
Do not carry out the correction of axial compression ratio.Formula (15) is applicable to two kinds of models, K simultaneously tDescending branch, K were arranged in＜0 o'clock tThere was not descending branch at＞0 o'clock.
Four, the derivation of displacement ductility
Displacement ductility is a parameter commonly used that is used for describing the ability of elastic-plastic deformation of member, and expression formula is μ=δ u/ δ y, δ yAnd δ uBe respectively the yield displacement and the extreme displacement of member.The displacement of yield load correspondence is yield displacement, definite often more complicated of yield point, and for structure or member that obvious flex point is arranged on load-displacement skeleton curve, flex point is yield point; When not having sharp yield point, yield displacement δ yTo follow the example of be the displacement of getting P-δ skeleton curve stretch section extensions and the point of intersection of tangents place of crossing peak point.Extreme displacement δ uGet bearing capacity and drop to the displacement of 85% o'clock correspondence of peak value carrying, do not have the member of descending branch for skeleton curve, the displacement when getting component damage is an extreme displacement.
The displacement ductility formula of reduction is derived
For the simplified model that descending branch is arranged, the computing formula of the skeleton curve simplified model that proposes according to last joint, the ductility factor of member is derived:
μ = δ u δ y = δ p - 0.15 × P y K t P y K a = δ p × K a P y - 0.15 × K a K t
= ( 0.5 n 2 - 0.98 n - 0.901 ) × ( 0.071 ξ - 0.953 ) × ( 0.097 λ / 20 + 1.727 ) -
0.15 [ 1.151 × ( 0.018 + 0.026 n 1 - 0.012 n 1 2 ) - 0.104 n 1 λ 2 f ck ( 1 - α ) + α f y E s - ( E s - E c ) ( 1 - α ) 2 ] - - - ( 16 )
In the formula: ξ=ξ s+ 0.5 * ξ f
For the model of no descending branch, ductility is enough good, does not consider the calculating of ductility factor.
The specific embodiment of the present invention is: steel pipe-FRP-concrete column capacity under axial determines that method is applied to steel pipe-FRP-concrete column.
Above content be in conjunction with concrete preferred implementation to further describing that the present invention did, can not assert that concrete enforcement of the present invention is confined to these explanations.For the general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, can also make some simple deduction or replace, all should be considered as belonging to protection scope of the present invention.

Claims (6)

1. steel pipe-FRP-concrete column capacity under axial is determined method, it is characterized in that, described steel pipe-FRP-concrete column is that the FPR pipe is set between the steel pipe of steel core concrete column and concrete, and steel pipe-FRP-concrete column capacity under axial determines that method comprises the steps:
Gather correlation parameter: gather the yield strength of steel in steel pipe-FRP-concrete, the hoop tensile strength and the concrete axial compressive strength of FRP pipe, gather steel pipe in the concrete filled steel tube, FRP pipe and concrete cross-sectional area.
Determine capacity under axial: N u=f ScA Sc, wherein: N uThe expression capacity under axial, A Sc=A s+ A c+ A f, ξ 1Cuff coefficient for steel pipe and FRP pipe satisfies ξ 1=(A sf y+ 0.5A ff h)/A cf Ck, A s, A f, A cBe respectively steel pipe, FRP pipe and concrete cross-sectional area; f y, f hAnd f CkBe respectively the yield strength of steel, the hoop tensile strength and the concrete axial compressive strength of FRP pipe.f Sc, A ScBe respectively the combination axial compressive strength and the cross-sectional area of member.
2. steel pipe according to claim 1-FRP-concrete column capacity under axial is determined method, it is characterized in that, in definite capacity under axial step, be included on the basis of steel core concrete column the cuff coefficient is revised to be suitable for steel pipe-FRP-concrete column.
3. steel pipe according to claim 2-FRP-concrete column capacity under axial is determined method, it is characterized in that, in definite capacity under axial step, comprise that structure steel pipe-FRP-concrete column model is to obtain on the basis of steel core concrete column the correction to the cuff coefficient.
4. steel pipe according to claim 3-FRP-concrete column capacity under axial is determined method, it is characterized in that, in definite capacity under axial step, making up steel pipe-FRP-concrete column model is the correction to skeleton curve restoring force model.
5. steel pipe according to claim 1-FRP-concrete column capacity under axial is determined method, it is characterized in that, in definite capacity under axial step, comprises steel pipe-FRP-concrete column displacement ductility is derived.
6. use steel pipe-FRP-concrete column that steel pipe-FRP-concrete column capacity under axial is determined method for one kind, it is characterized in that, steel pipe-FRP-concrete column capacity under axial determines that method is applied to steel pipe-FRP-concrete column.
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