CN102912936A - Method for designing FRP (fiber reinforce plastic) tube-concrete-steel tube combined column - Google Patents

Abstract

The invention discloses a design method for a novel combined component, and aims to provide a method for designing a FRP (fiber reinforce plastic) tube-concrete-steel tube combined column (hereinafter referred to as double-tube combined column). The design method is implemented through accurately evaluating whether the ultimate bearing capacity of the double-tube combined column meets the application requirement of an engineering component under the condition that the internal force value of the engineering component which is about to use the double-tube combined column is known. According to the invention, a design formula for calculating the compressive capacity of the normal section of the double-tube combined column is provided for the first time, and through combining the design formula with the existing formula for calculating the shear bearing capacity of an oblique section, the method can be applied to designs relatively accurately and partially safely. The formula takes a factor that the constraints of FRP tubes to concrete under an eccentric load are constantly changed into consideration, can be applied to the constraints of various types of FRP tubes, and keeps continuity with the existing FRP constrained reinforced concrete column formula in form. According to the invention, recommendations for the consumption of FRP tubes and the slenderness ratio range of components are put forward, so that the properties of materials in component design are fully used.

Description

The method for designing of FRP pipe-concrete-steel pipe zygostyle

Technical field

The present invention relates to a kind of method for designing of new structural members.More particularly, the present invention relates to a kind of for FRP pipe-concrete-steel pipe zygostyle method for designing of (being called for short two-tube coupled column).

Background technology

Continuous progress along with scientific and technical development and building trade, the combined member that takes full advantage of new type FRP (fibre reinforced plastics, Fiber Reinforced Plastics) composite material and traditional building material (as concrete) characteristics has become a kind of trend in the engineering application.FRP is a kind of Novel advanced composite material, good mechanical performance, and chemical stability is better.The tensile strength of FRP is very high, is at least the twice of structural steel, wherein CFRP(carbon fibre reinforced composite commonly used) can be up to ten times or more than; The density of FRP only has 1/5th of steel; The resistance to corrosion of FRP is strong, can intercept electromagnetic radiation, good endurance.The anti-fatigue ability of CFRP also is better than structural steel.Therefore, there is more obvious advantage in conjunction with other traditional materials such as utilizing new type FRP composite material ratio employing steel pipe in concrete component.

FRP pipe-concrete-steel pipe zygostyle is the new structural members begun one's study a kind of recent years, outside FRP pipe, inner steel pipe and middle concrete of filling, jointly consists of.The cross section of member can have according to the actual loading situation multiple multi-form.Owing to giving full play to FRP composite material, concrete, steel separately, this two-tube coupled column has the incomparable characteristics of some other members.As the FRP pipe is difficult for occurring cripling, its effect of contraction makes member have better ductility, under geological process, can be used as shear reinforcement, and the effect that prevents member generation brittle fracture is arranged, the FRP pipe has stronger decay resistance simultaneously, can be used as the permanent template of concreting in construction; The existence of the steel pipe of component inside, make member energy receiving portion give the load in man-hour, also more be convenient to bean column node or with basic being connected; The member cavity can be used as pipeline passway, and, because the cross section hollow rate ratio of external diameter (the concrete part internal diameter with) is usually desirable 0.6 ~ 0.8, has greatly alleviated the quality of member self.Existing test shows, the confined concrete bearing capacity of axial compression member can improve 3 ~ 4 times.The simple bending member is in the situation that depression of bearing force is very little, and mid-span deflection can reach 1/15 of span.These advantages, show that this two-tube coupled column has extraordinary application prospect.

But, in actual engineering design application, still there are the following problems: when making two-tube coupled column, still not accurately guidance method tell that the technician should its parameters of how to confirm, the application requirements that causes ultimate bearing capacity to two-tube coupled column whether can meet engineering component can't be estimated.And then cause blindly design, blindness to make and the blindness construction application, cause potential hazard finally to the engineering component quality.

Invention Inner holds

The technical problem to be solved in the present invention is, overcomes deficiency of the prior art, and the method for designing of a kind of FRP pipe-concrete-steel pipe zygostyle is provided, and makes design, the producer of two-tube coupled column obtain necessary suggestion accurately.

In order to solve the problems of the technologies described above, the present invention is achieved by the following technical solutions.

The invention provides the method for designing of a kind of FRP pipe-concrete-steel pipe zygostyle, described coupled column refers to by the steel pipe of outside FRP pipe, inside and is filled in the two-tube coupled column that the concrete between two pipes forms jointly; This method for designing is in the situation that the known internal force value that will use the engineering component of this two-tube coupled column, and whether the ultimate bearing capacity of the two-tube coupled column of accurate evaluation meets the application requirements of engineering component;

Definition is as follows in order to the parameter of describing two-tube coupled column: member length means with L; FRP pipe internal-and external diameter is respectively D and D _f, axial compression, ring draw modulus of elasticity to be respectively E _{xc, eff}, E _{θ t, eff}, actual rings is to breaking strain ε _ru; Middle concrete is without constraint and the lower peak strength difference of constraint f _co, f _cc, without lower strain corresponding to peak strength of constraint, be ε _co, initial elastic modulus is E _c, the limit compressive strain under simple bending is ε _{cu, b}; Inner outer diameter of steel pipes and thickness are respectively D _s, t _s, yield strength is f _y, modulus of elasticity is E _s.Member two ends eccentricity of loading is e ₁, e ₂, and agreement e ₂forever get on the occasion of and absolute value be greater than e ₁;

The method specifically comprises the following steps:

(1), for given two-tube coupled column, according to the bounds slenderness ratio design formulas, judge that two-tube coupled column belongs to short column or long column:

${\left(\frac{L}{D}\right)}_{\mathrm{cr}}={\mathrm{\η}}_1\frac{4+2.5(1+6\frac{e_2}{D})(1-\frac{e_1}{e_2})}{\frac{f_{\mathrm{cc}}}{f_{\mathrm{co}}}(1+0.05{\mathrm{\ρ}}_{\mathrm{\ϵ}})}$

In formula, ρ _εfor the FRP pipe ring to breaking strain than (ε _ru/ ε _co), η _?for considering hollow rate χ (=D _s/ D) corrected parameter of impact adopts following formula to calculate:

${\mathrm{\η}}_1={(1-\mathrm{\χ})}^{-0.16}$

If the L/D calculated value of designed component is less than bounds slenderness ratio (L/D) _crbe short column, otherwise be long column;

(2), for being judged as short column, adopt following formula to calculate the ultimate bearing capacity of two-tube coupled column:

$N_u={\mathrm{\α}}_1{f}_{\mathrm{cc},\mathrm{ec}}A[\mathrm{\θ}-\frac{\sin \left(2\mathrm{\π\θ}\right)}{2\mathrm{\π}}-{\mathrm{\χ}}^2{\mathrm{\θ}}^{\′}+{\mathrm{\χ}}^2\frac{\sin \left(2\mathrm{\π}{\mathrm{\θ}}^{\′}\right)}{2\mathrm{\π}}]+f_y{A}_s({\mathrm{\θ}}_c-{\mathrm{\θ}}_t)+\frac{5}{6}{\mathrm{\σ}}_f{A}_f{\mathrm{\θ}}_f$

$M_u=\frac{2}{3}{\mathrm{\α}}_1{f}_{\mathrm{cc},\mathrm{ec}}\mathrm{AR}[\frac{{\sin }^3\left(\mathrm{\π\θ}\right)}{\mathrm{\π}}-{\mathrm{\χ}}^3\frac{{\sin }^3\left(\mathrm{\π}{\mathrm{\θ}}^{\′}\right)}{\mathrm{\π}}]+f_y{A}_s{R}_s\frac{\sin \left(\mathrm{\π}{\mathrm{\θ}}_c\right)+\sin \left(\mathrm{\π}{\mathrm{\θ}}_t\right)}{\mathrm{\π}}+\frac{5}{6}\frac{{\mathrm{\σ}}_f{A}_{f}R}{\mathrm{\π}}{m}_f$

In formula, M _u, N _ufor eccentric distance e ₂the ultimate bearing capacity of lower member, R and R _sfor corresponding to D and D _ssection radius, A=π R ², A _f, A _sbe respectively the section area of FRP pipe, steel pipe; 2 π θ, 2 π θ ＇ are respectively the central angle of the corresponding FRP pipe of pressure zone concrete equivalent rectangular stress block height and steel pipe; Parameter alpha ₁, θ _c, θ _t, σ _f, θ _f, m _fby following calculating formula, obtain respectively:

${\mathrm{\α}}_1=1.16-0.18f_{\mathrm{cc},\mathrm{ec}}/f_{\mathrm{co}}$

$0\≤{\mathrm{\θ}}_c=1.25(\mathrm{\θ}-0.50)/\mathrm{\χ}+0.54\≤1$

$0\≤{\mathrm{\θ}}_t=-1.42(\mathrm{\θ}-0.44)/\mathrm{\χ}+0.53\≤1$

${\mathrm{\σ}}_f=E_{\mathrm{xc},\mathrm{eff}}{\mathrm{\ϵ}}_{\mathrm{cu},\mathrm{ec}}$

${\mathrm{\θ}}_f=0.75\mathrm{\θ}+0.03$

$\frac{f_{\mathrm{cc}}}{f_{\mathrm{co}}}<1.75$

In formula, ε _{cu, ec}, f _{cc, ec}being respectively eccentric throw is e ₂the time confined concrete limit compressive strain and ultimate strength, α ₁for the Average stress coefficient of confined concrete, and σ _ffor reaching strain stress _{cu, ec}the time FRP pipe compressive stress, all the other intermediate parameters that are computational process;

(3), for being judged as long column, adopt following formula to calculate the ultimate bearing capacity of two-tube coupled column:

$N_u={\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}A[\mathrm{\&theta;}-\frac{\sin \left(2\mathrm{\&pi;\&theta;}\right)}{2\mathrm{\&pi;}}-{\mathrm{\&chi;}}^2{\mathrm{\&theta;}}^{\&prime;}+{\mathrm{\&chi;}}^2\frac{\sin \left(2\mathrm{\&pi;}{\mathrm{\&theta;}}^{\&prime;}\right)}{2\mathrm{\&pi;}}]+f_y{A}_s({\mathrm{\&theta;}}_c-{\mathrm{\&theta;}}_t)+\frac{5}{6}{\mathrm{\&sigma;}}_f{A}_f{\mathrm{\&theta;}}_f$

$N_u{e}_{\max }=\frac{2}{3}{\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}^{\&prime;}\mathrm{AR}[\frac{{\sin }^3\left(\mathrm{\&pi;\&theta;}\right)}{\mathrm{\&pi;}}-{\mathrm{\&chi;}}^3\frac{{\sin }^3\left({\mathrm{\&pi;\&theta;}}^{\&prime;}\right)}{\mathrm{\&pi;}}]+f_y{A}_s{R}_s\frac{\sin \left(\mathrm{\&pi;}{\mathrm{\&theta;}}_c\right)+\sin \left({\mathrm{\&pi;\&theta;}}_t\right)}{\mathrm{\&pi;}}+\frac{5}{6}\frac{{\mathrm{\&sigma;}}_f{A}_{f}R}{\mathrm{\&pi;}}{m}_f$

In formula, parameter e _maxby following various calculating, obtain:

$N_{\mathrm{bal}}=\frac{0.5f_{\mathrm{cc}}{A}_o}{(1-0.75{\mathrm{\&chi;}}^2)}$

${\mathrm{\&zeta;}}_1=\frac{N_{\mathrm{bal}}}{N_u}\&le;1$

${\mathrm{\&zeta;}}_2=(1.15+0.07{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}})-(0.01+0.014{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}})\frac{L}{D}\&le;1$

$\mathrm{\&eta;}=1+\frac{1.25{\mathrm{\&epsiv;}}_{\mathrm{cu},,\mathrm{ec}}+0.0017}{8.5e_i/D}{\left(\frac{L}{D}\right)}^2{\mathrm{\&zeta;}}_1{\mathrm{\&zeta;}}_2$

$e_0=0.6e_2+0.4e_1\&GreaterEqual;0.4e_2$

$e_i=e_0+e_a$

$e_{\max }=\max \{{\mathrm{\&eta;e}}_i,e_2+e_a\}$

In formula, A _obe the total cross-sectional area that comprises FRP pipe, concrete, steel pipe, N _balsectional axis power while for boundary, destroying (tensile region and pressure zone destroy simultaneously), ζ ₁, ζ ₂the correction factor of member curvature and slenderness ratio while being respectively consideration destruction, η is the eccentric throw amplification coefficient, e ₀for equivalent eccentric throw, e _afor the accidental eccentricity of load action, the same reinforced concrete member of value;

(4) will calculate the ultimate bearing capacity of the two-tube coupled column obtained and will use the internal force value of the engineering component of this two-tube coupled column to compare, working as N _uwhile being less than or equal to the component internal force value, showing that the ultimate bearing capacity of this two-tube coupled column meets the application requirements of engineering component, otherwise be exactly not meet the demands.

In the present invention, described outside FRP caliber thickness rate (D _f/ t _f) get and be not more than 200.

In the present invention, described cross section concrete hollow rate χ (D _s/ D) value in 0.6 ~ 0.8 scope.

In the present invention, the radius-thickness ratio (D of described steel pipe _s/ t _s) be less than 70.

In the present invention, described member FRP consumption and member slenderness ratio adopt following formula to be limited:

$\frac{f_{\mathrm{cc}}}{f_{\mathrm{co}}}<1.75$

${(L/D)}_{\max }=12.5-{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}}$

In formula, the implication of each symbol is: f _cc/ f _cofor the ratio (mean FRP consumption how many) of concrete Constrained with unconfined peak strength, (L/D) _maxmember maximum slenderness-ratio for suggestion.

The invention has the beneficial effects as follows:

The present invention has proposed first for calculating the design formula of two-tube coupled column compressive load-carrying capacity of normal cross section, in conjunction with existing Shear Bearing Capacity Formula, formula has comprised the long and short post of two-tube combination and long and short post has been judged to whole process, can comparatively accurately and be partial to safely for design.Formula has considered that under eccentric load, the FRP pipe constantly changes this factor to the concrete constraint, and applicable to various types of FRP pipes (different kinds of fibers, prefabricated or later stage winding) constraint, continuity with existing FRP constraint steel concrete column formula keeps in form, make it easy to the designer and grasp and apply.The present invention advises to the effective amount of FRP and member slenderness ratio scope, and the performance of material in member designs is fully used, and reaches more economical, applicable purpose, and two-tube coupled column is made and proposed a series of useful suggestions.

The accompanying drawing explanation

The schematic cross-section that Fig. 1 is the concentric circles coupled column.

Fig. 2 is the schematic cross-section that outer tube is foursquare coupled column.

Fig. 3 is that inner and outer pipes is all the schematic cross-section of foursquare coupled column.

Fig. 4 is the two-tube coupled column schematic cross-section of non-concentric circles.

Fig. 5 is coupled column cross section and section stress rough schematic view.

Fig. 6 is the block diagram of the present invention for the detailed process of design.

The making flow chart that Fig. 7 is FRP pipe-concrete-steel pipe zygostyle.

Reference numeral in figure is: 1 FRP pipe; 2 concrete; 3 steel pipes; 4 well cabinet frames; 5 timber wedge; 6 pull bars; 7 carbon cloths; 8 node welds.

The specific embodiment

The two-tube coupled column the present invention relates to, FRP pipe 1 and steel pipe 3 are arranged in concentric circles, the prefabricated pipe that FRP pipe 1 is various different fibers and resin, inner steel pipe 3 is seamless steel pipe or welded steel pipe, and middle concrete 2 can be selected ordinary concrete or the contour performance concrete of self-compacting concrete according to space size.The present invention is based on the basic principle of fibre section method, according to existing test and theoretical research, consider the Mutability analysis combination dual string of 1 pair of inner concrete 2 effect of contraction of FRP pipe, propose to mean by 3 parts that are not coupled mutually the effect of FRP pipe 1, concrete 2, steel pipe 3, and form is succinct, the design formula of being convenient to application.Point out to make two-tube coupled column and must strictly control the relative position between outside FRP pipe 1 and inner steel pipe 3, reduce the deviation of structure manufacture, and the measure of taking a series of assurance bearing capacities to be not fully exerted.

The present invention is simplified interaction complicated between FRP pipe in two-tube coupled column 1, concrete 2 and steel pipe 3, suitable method for designing is proposed, both with existing FRP, retrained the reinforced concrete post design formula in principle and kept continuity in form, be convenient to the designer and use, take into full account again the reach capacity characteristics of state of each material of two-tube coupled column.

The present invention is the influence degree to element bearing capacity according to the load second-order effects, adopt different design formulas respectively long and short post to be designed, simultaneously for ease of design, propose the bounds slenderness ratio formula of reduction that the two-tube coupled column of judgement belongs to long column or short column, form the method that a ratio more completely calculates compressive load-carrying capacity of normal cross section.

The present invention manages 1 consumption (being the degree of restraint of FRP pipe 1) and requires to advise in the slenderness ratio that keeps FRP pipe 1 good binding effect prerequisite lower member FRP in two-tube coupled column.And, after whole method for designing, the method for making two-tube coupled column is concluded.

With reference to accompanying drawing, below describe the present invention.

Usually the parameter of describing two-tube coupled column is as follows: member length means with L; FRP manages 1 internal-and external diameter and is respectively D and D _f, axial compression, ring draw modulus of elasticity to be respectively E _{xc, eff}, E _{θ t, eff}, actual rings is to breaking strain ε _ru; Middle concrete 2 is without constraint and retrain lower peak strength f respectively _co, f _cc, without lower strain corresponding to peak strength of constraint, be ε _co, initial elastic modulus is E _c, the limit compressive strain under simple bending is ε _{cu, b}; Inner steel pipe 3 external diameters and thickness are respectively D _s, t _s, yield strength is f _y, modulus of elasticity is E _s.Member two ends eccentricity of loading is e ₁, e ₂, and agreement e ₂forever get on the occasion of and absolute value be greater than e ₁.For the requirement of sectional dimension, common outside FRP manages 1 radius-thickness ratio (D _f/ t _f) get and be not more than 200, the hollow rate χ (D of cross section concrete 2 _s/ D) value in 0.6 ~ 0.8 scope, the radius-thickness ratio (D of steel pipe 3 _s/ t _s) should be less than 70.

Method for designing of the present invention is taked following concrete operation step:

(1), at first for given two-tube coupled column, according to bounds slenderness ratio design formulas judgement member, belong to short column or long column:

${\left(\frac{L}{D}\right)}_{\mathrm{cr}}={\mathrm{\&eta;}}_1\frac{4+2.5(1+6\frac{e_2}{D})(1-\frac{e_1}{e_2})}{\frac{f_{\mathrm{cc}}}{f_{\mathrm{co}}}(1+0.05{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}})}$

In formula, ρ _εfor FRP manages 1 hoop breaking strain than (ε _ru/ ε _co); η ₁for considering the corrected parameter of hollow rate impact, adopt following formula to calculate.The L/D calculated value is less than (L/D) _cr, be short column, otherwise be long column.

${\mathrm{\&eta;}}_1={(1-\mathrm{\&chi;})}^{-0.16}$

(2), for being judged as short column, can adopt following formula to calculate the ultimate bearing capacity of member:

$N_u={\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}A[\mathrm{\&theta;}-\frac{\sin \left(2\mathrm{\&pi;\&theta;}\right)}{2\mathrm{\&pi;}}-{\mathrm{\&chi;}}^2{\mathrm{\&theta;}}^{\&prime;}+{\mathrm{\&chi;}}^2\frac{\sin \left(2\mathrm{\&pi;}{\mathrm{\&theta;}}^{\&prime;}\right)}{2\mathrm{\&pi;}}]+f_y{A}_s({\mathrm{\&theta;}}_c-{\mathrm{\&theta;}}_t)+\frac{5}{6}{\mathrm{\&sigma;}}_f{A}_f{\mathrm{\&theta;}}_f$

$M_u=\frac{2}{3}{\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}\mathrm{AR}[\frac{{\sin }^3\left(\mathrm{\&pi;\&theta;}\right)}{\mathrm{\&pi;}}-{\mathrm{\&chi;}}^3\frac{{\sin }^3\left(\mathrm{\&pi;}{\mathrm{\&theta;}}^{\&prime;}\right)}{\mathrm{\&pi;}}]+f_y{A}_s{R}_s\frac{\sin \left(\mathrm{\&pi;}{\mathrm{\&theta;}}_c\right)+\sin \left(\mathrm{\&pi;}{\mathrm{\&theta;}}_t\right)}{\mathrm{\&pi;}}+\frac{5}{6}\frac{{\mathrm{\&sigma;}}_f{A}_{f}R}{\mathrm{\&pi;}}{m}_f$

M in formula _u, N _ufor eccentric distance e ₂the ultimate bearing capacity of lower member, R and R _sfor corresponding to D and D _ssection radius, A=π R ², A _f, A _sbe respectively the section area of FRP pipe 1, steel pipe 3.2 π θ, 2 π θ ＇ are respectively the central angle of the corresponding FRP pipe 1 of pressure zone concrete 2 equivalent rectangular stress block height and steel pipe 3, other parameter alpha ₁, θ _c, θ _t, σ _f, θ _f, m _fbe respectively calculated as follows

${\mathrm{\&alpha;}}_1=1.16-0.18f_{\mathrm{cc},\mathrm{ec}}/f_{\mathrm{co}}$

$0\&le;{\mathrm{\&theta;}}_c=1.25(\mathrm{\&theta;}-0.50)/\mathrm{\&chi;}+0.54\&le;1$

$0\&le;{\mathrm{\&theta;}}_t=-1.42(\mathrm{\&theta;}-0.44)/\mathrm{\&chi;}+0.53\&le;1$

${\mathrm{\&sigma;}}_f=E_{\mathrm{xc},\mathrm{eff}}{\mathrm{\&epsiv;}}_{\mathrm{cu},\mathrm{ec}}$

${\mathrm{\&theta;}}_f=0.75\mathrm{\&theta;}+0.03$

$m_f=\sin \left({\mathrm{\&pi;\&theta;}}_f\right)$

ε in formula _{cu, b}, f _{cc, ec}being respectively eccentric throw is e ₂the time confined concrete 2 limit compressive strain and ultimate strength, α ₁for the Average stress coefficient of confined concrete 2, and σ _ffor reaching strain stress _{cu, ec}the time FRP pipe 1 compressive stress, all the other intermediate parameters that are computational process.

(3), for being judged as long column, can adopt following formula to calculate the ultimate bearing capacity of member:

$N_u={\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}A[\mathrm{\&theta;}-\frac{\sin \left(2\mathrm{\&pi;\&theta;}\right)}{2\mathrm{\&pi;}}-{\mathrm{\&chi;}}^2{\mathrm{\&theta;}}^{\&prime;}+{\mathrm{\&chi;}}^2\frac{\sin \left(2\mathrm{\&pi;}{\mathrm{\&theta;}}^{\&prime;}\right)}{2\mathrm{\&pi;}}]+f_y{A}_s({\mathrm{\&theta;}}_c-{\mathrm{\&theta;}}_t)+\frac{5}{6}{\mathrm{\&sigma;}}_f{A}_f{\mathrm{\&theta;}}_f$

$N_u{e}_{\max }=\frac{2}{3}{\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}^{\&prime;}\mathrm{AR}[\frac{{\sin }^3\left(\mathrm{\&pi;\&theta;}\right)}{\mathrm{\&pi;}}-{\mathrm{\&chi;}}^3\frac{{\sin }^3\left({\mathrm{\&pi;\&theta;}}^{\&prime;}\right)}{\mathrm{\&pi;}}]+f_y{A}_s{R}_s\frac{\sin \left(\mathrm{\&pi;}{\mathrm{\&theta;}}_c\right)+\sin \left({\mathrm{\&pi;\&theta;}}_t\right)}{\mathrm{\&pi;}}+\frac{5}{6}\frac{{\mathrm{\&sigma;}}_f{A}_{f}R}{\mathrm{\&pi;}}{m}_f$

Parameter e in formula _maxcan be by following various calculating

$N_{\mathrm{bal}}=\frac{0.5f_{\mathrm{cc}}{A}_o}{(1-0.75{\mathrm{\&chi;}}^2)}$

${\mathrm{\&zeta;}}_1=\frac{N_{\mathrm{bal}}}{N_u}\&le;1$

${\mathrm{\&zeta;}}_2=(1.15+0.07{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}})-(0.01+0.014{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}})\frac{L}{D}\&le;1$

$\mathrm{\&eta;}=1+\frac{1.25{\mathrm{\&epsiv;}}_{\mathrm{cu},\mathrm{ec}}+0.0017}{8.5e_i/D}{\left(\frac{L}{D}\right)}^2{\mathrm{\&zeta;}}_1{\mathrm{\&zeta;}}_2$

$e_0=0.6{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002262779400011.png,HDA00002262779400012.png"\; state="\{\{state\}\}">e</figure-callout>}}_2+0.4{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA00002262779400011.png,HDA00002262779400012.png"\; state="\{\{state\}\}">e</figure-callout>}}_1\&GreaterEqual;0.4{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002262779400011.png,HDA00002262779400012.png"\; state="\{\{state\}\}">e</figure-callout>}}_2$

$e_i=e_0+e_a$

$e_{\max }=\max \{\mathrm{\&eta;}{e}_i,e_2+e_a\}$

In formula, A _obe the total cross-sectional area that comprises FRP pipe 1, concrete 2, steel pipe 3, N _balsectional axis power while for boundary, destroying (tensile region and pressure zone destroy simultaneously), ζ ₁, ζ ₂the correction factor of member curvature and slenderness ratio while being respectively consideration destruction, η is the eccentric throw amplification coefficient, e ₀for equivalent eccentric throw, e _afor the accidental eccentricity of load action, the same reinforced concrete member of value.

(4) will calculate the ultimate bearing capacity of the two-tube coupled column obtained and will use the internal force value of the engineering component of this two-tube coupled column to compare, working as N _uwhile being less than or equal to the component internal force value, showing that the ultimate bearing capacity of this two-tube coupled column meets the application requirements of engineering component, otherwise be exactly not meet the demands.

In practical application, following two different modes are often arranged: the one, the parameters of known members solves ultimate bearing capacity, process as previously described.

Another way is exactly to calculate conversely according to analyzing resulting internal force value the size of determining member.At this moment reasonably the selection of scantling is just important, and the present invention advises adopting following formula to be limited member FRP consumption and member slenderness ratio:

$\frac{f_{\mathrm{cc}}}{f_{\mathrm{co}}}<1.75$

${(L/D)}_{\max }=13.5-{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}}$

Above formula adopted the ratio value representation FRP consumption of lower concrete 2 peak strengths of constraint with without constraint the time the number.

The calculating of two-tube coupled column Shear bearing capacity can be joined " fibre reinforced composites construction work application technology standard ".The step of utilizing the present invention to advise that formula is designed can be referring to accompanying drawing.

After the size of two-tube coupled column is determined in design, Specific construction is exactly next step, mainly comprises following 5 steps: inner steel pipe 3 is fixing; FRP pipe 1 and steel pipe 3 relative positions are fixed; Concrete 2 is built; Form removal and strengthening member; Node connects to be processed.Fixedly the relative position of FRP pipe 1 and steel pipe 3 can adopt diagram well cabinet frame 4, timber wedge 5 to add the aids such as vertical pull bar 6, can push down FRP pipe 1 simultaneously and prevent that it from changing building middle position.The concrete 2 of building should be self-compacting concrete or mobility commercial concrete preferably.After treating the member form removal, be wrapped with the high-strength materials such as carbon cloth 7 at the two ends of member and prevent that end from destroying too early.The connector that on the last steel pipe outstanding in inside, welding and beam etc. are connected, should carry out certain reinforcement at the position of joints of connection.

Application example of the present invention:

Embodiment mono-(known sectional dimension is calculated the member ultimate bearing capacity):

According to the data of certain test, the sectional dimension of two-tube coupled column etc. are as follows: two-tube coupled column length L=465mm, the outside CFRP of winding cloth forms FRP pipe 1, D outer diameter _f=155mm, thickness t _f=0.17mm, elastic modulus in circular direction E _{θ t, eff}=80.1GPa, axial rigidity is ignored, hoop actual crack strain stress _ru=0.0196, concrete 2 is without constraint peak strength f _co=45.6, corresponding strain stress _co=0.0245, inner steel pipe 3 D outer diameter _s=76mm, wall thickness t _s=3.7mm, yield strength f _y=398.2MPa.The eccentric distance e of load action ₂=18mm.

According to bounds slenderness ratio formula (L/D) _cr=3.18>465/155=3, but therefore determination means is short column.The design formula of the two-tube short composite columns of substitution is calculated, and finally calculates this member ultimate bearing capacity N _u=702.56kN.And the result of test, this member ultimate bearing capacity is 709.3kN, both differ only 1% left and right, have illustrated that design formula has good precision.

Embodiment bis-(known calculations internal force is determined the size of member):

A certain bridge engineering pier column, routine analyzer obtains cross section internal force: N=46180kN, M=16671kNm, V=21082kN, the high 7.6m of pier column.Adopt the GFRP pipe according to project situation, just determine D outer diameter _f=2000mm, wall thickness t _f=20mm, FRP manages 80 ° of 1 Filament-wound Machine angles, and its material property is as follows: E _{θ t, eff}=42GPa, E _{xc, eff}=6GPa, calculate hoop breaking strain ε _ru=0.0074.Middle concrete 2 adopts C40, strain stress _coget 0.002, inner steel pipe 3 external diameters are D _s=1200mm, wall thickness t _s=30mm, yield strength f _y=205MPa(is according to after standard GB50608 reduction), modulus of elasticity is 200GPa, eccentric throw is pressed e ₂=M/N=361mm calculates.

Calculate the bounds slenderness ratio (L/D) of member _cr=2.37<7600/2000=3.8, can be designed by long column.With e ₂=361mm substitution long column design formulas, finally calculate element bearing capacity N _u=58129kN>N, normal section bearing capacity meets the demands.For sloping section, by standard GB50608 7.2.5 bar, V _f=32930kN>V, even if do not consider steel pipe 3 and concrete 2, the shear-carrying capacity that only calculates the GFRP pipe is just enough.Therefore, can adopt above-mentioned design result.Certainly, this result has the place that can optimize, should incorporation engineering is actual carries out.

Claims (5)

1. the method for designing of FRP pipe-concrete-steel pipe zygostyle, described coupled column refers to by outside FRP pipe, inner steel pipe and is filled in the two-tube coupled column that the concrete between two pipes forms jointly; It is characterized in that, this method for designing is in the situation that the known internal force value that will use the engineering component of this two-tube coupled column, and whether the ultimate bearing capacity of the two-tube coupled column of accurate evaluation meets the application requirements of engineering component;

Definition is as follows in order to the parameter of describing two-tube coupled column: member length means with L; FRP pipe internal-and external diameter is respectively D and D _f, axial compression, ring draw modulus of elasticity to be respectively E _{xc, eff}, E _{θ t, eff}, actual rings is to breaking strain ε _ru; Middle concrete is without constraint and the lower peak strength difference of constraint f _co, f _cc, without lower strain corresponding to peak strength of constraint, be ε _co, initial elastic modulus is E _c, the limit compressive strain under simple bending is ε _{cu, b}; Inner outer diameter of steel pipes and thickness are respectively D _s, t _s, yield strength is f _y, modulus of elasticity is E _s; Member two ends eccentricity of loading is e ₁, e ₂, and agreement e ₂forever get on the occasion of and absolute value be greater than e ₁;

The method specifically comprises the following steps:

(1), for given two-tube coupled column, according to the bounds slenderness ratio design formulas, judge that two-tube coupled column belongs to short column or long column:

${\left(\frac{L}{D}\right)}_{\mathrm{cr}}={\mathrm{\&eta;}}_1\frac{4+2.5(1+6\frac{e_2}{D})(1-\frac{e_1}{e_2})}{\frac{f_{\mathrm{cc}}}{f_{\mathrm{co}}}(1+0.05{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}})}$

In formula, _?for the FRP pipe ring to breaking strain than (ε _ru/ ε _co), η _?for considering hollow rate (=D _s/ D) corrected parameter of impact adopts following formula to calculate:

${\mathrm{\&eta;}}_1={(1-\mathrm{\&chi;})}^{-0.16}$

If the L/D calculated value of designed component is less than bounds slenderness ratio (L/D) _crbe short column, otherwise be long column;

(2), for being judged as short column, adopt following formula to calculate the ultimate bearing capacity of two-tube coupled column:

$N_u={\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}A[\mathrm{\&theta;}-\frac{\sin \left(2\mathrm{\&pi;\&theta;}\right)}{2\mathrm{\&pi;}}-{\mathrm{\&chi;}}^2{\mathrm{\&theta;}}^{\&prime;}+{\mathrm{\&chi;}}^2\frac{\sin \left(2\mathrm{\&pi;}{\mathrm{\&theta;}}^{\&prime;}\right)}{2\mathrm{\&pi;}}]+f_y{A}_s({\mathrm{\&theta;}}_c-{\mathrm{\&theta;}}_t)+\frac{5}{6}{\mathrm{\&sigma;}}_f{A}_f{\mathrm{\&theta;}}_f$

$M_u=\frac{2}{3}{\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}\mathrm{AR}[\frac{{\sin }^3\left(\mathrm{\&pi;\&theta;}\right)}{\mathrm{\&pi;}}-{\mathrm{\&chi;}}^3\frac{{\sin }^3\left(\mathrm{\&pi;}{\mathrm{\&theta;}}^{\&prime;}\right)}{\mathrm{\&pi;}}]+f_y{A}_s{R}_s\frac{\sin \left(\mathrm{\&pi;}{\mathrm{\&theta;}}_c\right)+\sin \left(\mathrm{\&pi;}{\mathrm{\&theta;}}_t\right)}{\mathrm{\&pi;}}+\frac{5}{6}\frac{{\mathrm{\&sigma;}}_f{A}_{f}R}{\mathrm{\&pi;}}{m}_f$

In formula, M _u, N _ufor eccentric distance e ₂the ultimate bearing capacity of lower member, R and R _sfor corresponding to D and D _ssection radius, A=π R ², A _f, A _sbe respectively the section area of FRP pipe, steel pipe; 2 π θ, 2 π θ ＇ are respectively the central angle of the corresponding FRP pipe of pressure zone concrete equivalent rectangular stress block height and steel pipe; Parameter alpha ₁, θ _c, θ _t, σ _f, θ _f, m _fby following calculating formula, obtain respectively:

${\mathrm{\&sigma;}}_1=1.16-0.18f_{\mathrm{cc},\mathrm{ec}}/f_{\mathrm{co}}$

$0\&le;{\mathrm{\&theta;}}_c=1.25(\mathrm{\&theta;}-0.50)/\mathrm{\&chi;}+0.54\&le;1$

$0\&le;{\mathrm{\&theta;}}_t=-1.42(\mathrm{\&theta;}-0.44)/\mathrm{\&chi;}+0.53\&le;1$

${\mathrm{\&sigma;}}_f=E_{\mathrm{xc},\mathrm{eff}}{\mathrm{\&epsiv;}}_{\mathrm{cu},\mathrm{ec}}$

${\mathrm{\&theta;}}_f=0.75\mathrm{\&theta;}+0.03$

$m_f=\sin \left(\mathrm{\&pi;}{\mathrm{\&theta;}}_f\right)$

In formula, ε _{cu, ec}, f _{cc, ec}being respectively eccentric throw is e ₂the time confined concrete limit compressive strain and ultimate strength, α ₁for the Average stress coefficient of confined concrete, and σ _ffor reaching strain stress _{cu, ec}the time FRP pipe compressive stress, all the other intermediate parameters that are computational process;

(3), for being judged as long column, adopt following formula to calculate the ultimate bearing capacity of two-tube coupled column:

$N_u={\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}A[\mathrm{\&theta;}-\frac{\sin \left(2\mathrm{\&pi;\&theta;}\right)}{2\mathrm{\&pi;}}-{\mathrm{\&chi;}}^2{\mathrm{\&theta;}}^{\&prime;}+{\mathrm{\&chi;}}^2\frac{\sin \left(2\mathrm{\&pi;}{\mathrm{\&theta;}}^{\&prime;}\right)}{2\mathrm{\&pi;}}]+f_y{A}_s({\mathrm{\&theta;}}_c-{\mathrm{\&theta;}}_t)+\frac{5}{6}{\mathrm{\&sigma;}}_f{A}_f{\mathrm{\&theta;}}_f$

$N_u{e}_{\max }=\frac{2}{3}{\mathrm{\&alpha;}}_1{f}_{\mathrm{cc},\mathrm{ec}}^{\&prime;}\mathrm{AR}[\frac{{\sin }^3\left(\mathrm{\&pi;\&theta;}\right)}{\mathrm{\&pi;}}-{\mathrm{\&chi;}}^3\frac{{\sin }^3\left({\mathrm{\&pi;\&theta;}}^{\&prime;}\right)}{\mathrm{\&pi;}}]+f_y{A}_s{R}_s\frac{\sin \left(\mathrm{\&pi;}{\mathrm{\&theta;}}_c\right)+\sin \left({\mathrm{\&pi;\&theta;}}_t\right)}{\mathrm{\&pi;}}+\frac{5}{6}\frac{{\mathrm{\&sigma;}}_f{A}_{f}R}{\mathrm{\&pi;}}{m}_f$

In formula, parameter e _maxby following various calculating, obtain:

$N_{\mathrm{bal}}=\frac{0.5f_{\mathrm{cc}}{A}_o}{(1-0.75{\mathrm{\&chi;}}^2)}$

${\mathrm{\&zeta;}}_1=\frac{N_{\mathrm{bal}}}{N_u}\&le;1$

${\mathrm{\&zeta;}}_2=(1.15+0.07{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}})-(0.01+0.014{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}})\frac{L}{D}\&le;1$

$\mathrm{\&eta;}=1+\frac{1.25{\mathrm{\&epsiv;}}_{\mathrm{cu},,\mathrm{ec}}+0.0017}{8.5e_i/D}{\left(\frac{L}{D}\right)}^2{\mathrm{\&zeta;}}_1{\mathrm{\&zeta;}}_2$

$e_0=0.6e_2+0.4e_1\&GreaterEqual;0.4e_2$

$e_i=e_0+e_a$

$e_{\max }=\max \{{\mathrm{\&eta;e}}_i,e_2+e_a\}$

In formula, A _obe the total cross-sectional area that comprises FRP pipe, concrete, steel pipe, N _balsectional axis power while for boundary, destroying (tensile region and pressure zone destroy simultaneously), ζ ₁, ζ ₂the correction factor of member curvature and slenderness ratio while being respectively consideration destruction, η is the eccentric throw amplification coefficient, e ₀for equivalent eccentric throw, e _afor the accidental eccentricity of load action, the same reinforced concrete member of value;

(4) will calculate the ultimate bearing capacity of the two-tube coupled column obtained and will use the internal force value of the engineering component of this two-tube coupled column to compare, working as N _uwhile being less than or equal to the component internal force value, showing that the ultimate bearing capacity of this two-tube coupled column meets the application requirements of engineering component, otherwise be exactly not meet the demands.

2. method for designing according to claim 1, is characterized in that, described outside FRP caliber thickness rate (D _f/ t _f) get and be not more than 200.

3. method for designing according to claim 1, is characterized in that, described cross section concrete hollow rate χ (D _s/ D) value in 0.6 ~ 0.8 scope.

4. method for designing according to claim 1, is characterized in that, the radius-thickness ratio (D of described steel pipe _s/ t _s) be less than 70.

5. according to the described method for designing of claim 1 to 4 any one, it is characterized in that, described member FRP consumption and member slenderness ratio adopt following formula to be limited:

$\frac{f_{\mathrm{cc}}}{f_{\mathrm{co}}}<1.75$

${(L/D)}_{\max }=13.5-{\mathrm{\&rho;}}_{\mathrm{\&epsiv;}}$

In formula, the implication of each symbol is: f _cc/ f _cofor the ratio (mean FRP consumption how many) of concrete Constrained with unconfined peak strength, (L/D) _maxmember maximum slenderness-ratio for suggestion.

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