CN105279325A - Method for calculating equivalent calculation length and stability of steel tube concrete tapered column in view of integral space action - Google Patents

Abstract

The invention discloses a method for calculating equivalent calculation length and stability of a steel tube concrete tapered column in view of an integral space action, and belongs to the field of steel tube concrete tapered column design. The method comprises the steps of: calculating an eigenvalue load of the steel tube concrete tapered column in view of the integral space action through finite element software, performing eigenvalue buckling analysis on a column with two hinged ends without the space action, and analyzing a buckling eigenvalue of a column with two hinged ends, a small head and a uniform section without the space action; calculating a calculation length coefficient of a supporting column in view of an integral space restriction action; obtaining an equivalent calculation length coefficient of the steel tube concrete tapered column with two hinged ends under an equivalent uniform-section column; and obtaining an equivalent calculation length coefficient of the tapered column in view of the integral space action. The invention provides a judgment method for the equivalent calculation length and stability of the steel tube concrete tapered column in view of the integral space action, so that a practical, efficient and accurate engineering application calculation method is obtained.

Description

Consider concrete filled steel tube tapered pole Equivalent Calculation length and the calculation method for stability of monolithic space action

Technical field

The invention belongs to concrete filled steel tube tapered pole design field.

Background technology

Concrete filled steel tube tapered pole as important structural support members, usually adopt by large complicated large span spatial structure, therefore the design and calculation method of its stability bearing capacity is extremely important.But existing specification is not made an explanation to concrete filled steel tube tapered pole computational length coefficient calculations, more it is not made an explanation in the differentiation of consideration monolithic space action stability inferior, the component model of the consideration stability that reason to be specification be convenience of calculation is all is areal model, and does not adopt spatial model.The method of current engineering application: under often kind of load mode, the stability bearing capacity that every single order buckling mode goes for each pillar obtains the computational length coefficient of each pillar, reach and consider space mass action, but quite loaded down with trivial details to labyrinth, and impracticable.Therefore, in current engineering, there is no to concrete filled steel tube tapered pole stability bearing capacity under structure monolithic space action that it carries out the problem of rational design & check.

Summary of the invention

The object of the invention is to: solve the problem of prior art, and propose conical steel pipe concrete column Equivalent Calculation length and the Convenient stable criterion of a set of consideration monolithic space action, thus obtain a set of practicality, efficiently, engineer applied computing method accurately.

The object of the invention is realized by following technical proposals:

Consider concrete filled steel tube tapered pole Equivalent Calculation length and the calculation method for stability of monolithic space action, it is characterized in that step is:

(1) the concrete filled steel tube tapered pole eigenwert load N considering monolithic space action is calculated by finite element software _cr, without the Eigenvalue Buckling Analysis N of the pin-ended post of space behavior _cr0, and the buckling eigenvalue N of pin-ended microcephaly column with constant cross sections without space behavior _cr0';

Specifically, its alternative operation modes is: for considering space behavior, in finite element software, set up block mold, then by the target post emission levels constraint in model, go out with the buckling analysis function calculating of software the eigenwert load N that target post concrete filled steel tube tapered pole considers monolithic space action _cr, then with the hinged concrete filled steel tube tapered pole in the single two ends of buckling analysis functional analysis namely without the Eigenvalue Buckling Analysis N of the pin-ended post of space behavior _cr0, in like manner analyze the buckling eigenvalue N of the pin-ended microcephaly column with constant cross sections without space behavior _cr0'; Existing various finite element software all can use, the general finite meta softwares such as such as SAP2000, ANSYS.

(2) by following formula, the support column computational length coefficient μ considering the overall effect of contraction in space is tried to achieve:

$\mathrm{\μ}=\sqrt{\frac{N_{cr0}}{N_{cr}}};$

(3) the equivalent calculated length coefficient μ of concrete filled steel tube tapered pole under equivalent column with constant cross sections that two ends are hinged as follows, is drawn _eff0:

${\mathrm{\μ}}_{eff0}=\sqrt{\frac{{N_{cr0}}^{\′}}{N_{cr0}}};$

(4) the equivalent calculated length coefficient μ that column with variable cross-sections considers monolithic space action as follows, is obtained _eff:

μ _eff＝μμ _eff0；

(5) by " concrete filled steel tube technical regulation: CECS28-2012 " regulation, the tapered pole above-mentioned derivation drawn considers the equivalent calculated length coefficient μ of monolithic space action _effsubstitute into 5.1.3 bar, 5.1.4 bar, the press-bending stability bearing capacity of carrying out concrete filled steel tube tapered pole is checked.In this step, equivalent calculated length coefficient being brought into the reason that " concrete filled steel tube technical regulation " carry out checking is that code has examined the various initial imperfection of worry component and primary stress, and calculate safer, simple to operate, application is strong.

Key of the present invention is:

1. the precondition of existing specification and written books paper stability Calculation is all based on supposition, and the computing unit studied is all planar structures, but for practical structures, version is three-dimensional, and the difference of structural system, load, constraint, and the boundary condition of structural elements varies, unstable phenomenon is had nothing in common with each other, practical structures is simulated by finite element model, this avoid condition hypothesis, and structural model used is directly the space structure considering each component, the actual space behavior simulated suffered by component.

2. the method is applicable to the concrete filled steel tube tapered pole that all section radius linearly change, the special-shaped column with variable cross-sections of other type inapplicable.

3. the theoretical foundation of invention derives the Bearing Capacity Formula under concrete filled steel tube tapered pole monolithic stability similar to the formula of Euler's critical force of column with constant cross sections.

4. the stability bearing capacity value N of same concrete filled steel tube taper surface post _crlinearly change under various boundary conditions.

5. the concrete filled steel tube tapered pole eigenwert load N considering monolithic space action is calculated at finite element software _crbe by discharge in block mold the horizontal degree of freedom of target steel core concrete column upper horizontal then buckling analysis obtain.

Beneficial effect of the present invention:

The inventive method with the accurate buckling analysis of large space Finite Element Eigenvalue for instrument, based on elastic stability theory, the stability Design formula of the existing design specifications of integrated use, propose the designing and calculating length calculation method of concrete filled steel tube tapered pole and a whole set of calculation procedure of calculating steady bearing capacity and method of considering monolithic space action, reasonably check for concrete filled steel tube tapered pole and provide computing method and support with design.Invention has important engineering practical value and social benefit significantly.

Computing method of the present invention, are not only applicable to general high level, super-high building structure, are suitable for Pressures On Complex Large-span degree space grid structure yet, and final equivalent result check combines with existing general specification, for engineering calculation provides effective and reliable method.

Accompanying drawing explanation

Fig. 1 is pin-ended tapered pole balance differential equation computation model;

Fig. 2 is existing shape specification plane framework side moves unstability aspect graph;

Fig. 3 is existing shape specification side moves unstability column length coefficient calculations sketch;

Fig. 4 is the buckling mode of target post eigenwert critical load Ncr and correspondence;

Fig. 5 is the target post in Fig. 4;

Fig. 6 is the pin-ended tapered pole buckling mode of target post without space behavior;

Fig. 7 is the eigenvalue buckling mode of pin-ended microcephaly column with constant cross sections;

Fig. 8 is that N-M ultimate bearing is tried hard to;

Fig. 9 is calculation flow chart of the present invention;

Figure 10 is analysis schematic diagram of the present invention.

Embodiment

Following non-limiting examples is for illustration of the present invention.

Column with constant cross sections Euler's formula is only had in prior art, the computing formula of the tapered pole of the variable cross section that not the present invention is directed to, therefore the present inventor has done following derivation proves, proves that the Bearing Capacity Formula under steel core concrete column monolithic stability is similar to the formula of Euler's critical force of column with constant cross sections:

The critical bearing capacity N of axial compression eigenwert of pin-ended tapered pole _cr0theory deduction:

Balance differential equation is set up:

Without loss of generality, the balance differential equation of pin-ended taper column with variable cross-sections is:

$EI\left(x\right)\frac{d^{2}y}{{\mathrm{dx}}^2}+P_{1}y=0---(1-1)$

$EI\left(x\right)\frac{d^{2}y}{{\mathrm{dx}}^2}+Py=0$

E is elastic modulus, the moment of inertia that I (x) is tapered pole, and P is axial pressure, and y is horizontal direction amount of deflection, and origin is at conial vertex place

Pin-ended tapered pole as shown in Figure 1, l in Fig. 1 ₀for pillar top is to the distance of conial vertex, l is the physical length of pillar, set up as Fig. 1 rectangular axes, the sectional dimension of the hinged axial compression taper in two ends round steel post is along mast axis linear change, and its cross sectional moment of inertia presses the biquadratic relationship change of radius along axis.

Computation model as Fig. 1, the equilibrium establishment differential equation:

${\mathrm{Ekx}}^4\frac{d^{2}w}{{\mathrm{dx}}^2}+Pw=0---(1-2)$

Wherein, w is y direction camber, because y relates to formula variable computing below, so place is moment of inertia variation factor without y, k, is a constant.Then the top of taper variable cross section round steel post and the moment of inertia of bottom have I respectively ₁=k (l ₀+ l) ⁴and I ₀=kl ₀ ⁴.Note μ ²=P/ (Ek), therefore the above-mentioned differential equation can be deformed into

$\frac{d^{2}w}{{\mathrm{dt}}^2}+\frac{2}{t}\frac{dw}{dt}+{\mathrm{\μ}}^{2}w=0---(1-3)$

Balance differential equation solves:

Consider following Second Order Linear Differential Equation with Variable Coefficients

x ²y”+[2x ²G(x)+x]y'+[x ²G'(x)+x ²G ²(x)+xG(x)+λ ²x ²-n ²]y＝0

The linear change of unknown function can turn to the Bessel's equation of empty argument, converts:

y＝e ^-∫G(x)dxu(x)

Change function y into u, then have

x ²u”+xu'+(λ ²x ²-n ²)u＝0

Remake conversion

t＝λx

And remember

$v\left(t\right)=u\left(\frac{t}{\mathrm{\λ}}\right)$

Thus obtain

t ²v”+xv'+(t ²-n ²)v＝0

Equation take v as the Bessel's equation of the empty argument of unknown function

So, order $w=e^{-\∫G\left(t\right)dt}u\left(t\right),$ Be easy to get $G\left(t\right)=\frac{1}{t}$

Therefore have:

$w=e^{-\∫G\left(t\right)dt}u\left(t\right)=t^{-\frac{1}{2}}u\left(t\right)$

$w^{\′}={\[t^{-\frac{1}{2}}u\left(t\right)\]}^{\′}=-\frac{1}{2}{t}^{-\frac{3}{2}}u\left(t\right)+t^{-\frac{1}{2}}{u}^{\′}\left(t\right)$

$w^{\′\′}={\[t^{-\frac{1}{2}}u\left(t\right)\]}^{\′\′}=\frac{3}{4}{t}^{-\frac{5}{2}}u\left(t\right)-t^{-\frac{3}{2}}{u}^{\′}\left(t\right)+t^{-\frac{1}{2}}{u}^{\′\′}\left(t\right)$

Then equation (1-3) is deformed into:

${\[t^{-\frac{1}{2}}u\left(t\right)\]}^{\′\′}+\frac{2}{t}{\[t^{-\frac{1}{2}}u\left(t\right)\]}^{\′}+{\mathrm{\μ}}^2{t}^{-\frac{1}{2}}u\left(t\right)=0$

$t^2{u}^{\′\′}+{\mathrm{tu}}^{\′}\left(t\right)+\[\frac{{\mathrm{Pa}}^4}{{\mathrm{EI}}_1}{t}^2-{\left(\frac{1}{2}\right)}^2\]u\left(t\right)=0$

${\[t^{-\frac{1}{2}}u\left(t\right)\]}^{\′\′}+\frac{2}{t}{\[t^{-\frac{1}{2}}u\left(t\right)\]}^{\′}+{\mathrm{\μ}}^2{t}^{-\frac{1}{2}}u\left(t\right)=0$

$t^2{u}^{\′\′}+{\mathrm{tu}}^{\′}\left(t\right)+\[\frac{{{\mathrm{Pl}}_0}^4}{{\mathrm{EI}}_1}{t}^2-{\left(\frac{1}{2}\right)}^2\]u\left(t\right)=0$

Order $k^2=\frac{{{\mathrm{Pl}}_0}^4}{{\mathrm{EI}}_1}{t}^2,v\left(k\right)=u\left(t\right)$

Above formula can be deformed into

$k^2{v}^{\′\′}\left(k\right)+2{\mathrm{kv}}^{\′}\left(k\right)+\left(\frac{1}{4}-k^2\right)v\left(k\right)=0---\left(2-1\right)$

According to " Equations of Mathematical Physics and special function " (Wang Yuanming. Equations of Mathematical Physics and special function [M]. Beijing: Higher Education Publishing House, 2004.1:130-145) solve

$\left(k\right)={\mathrm{AJ}}_{-\frac{1}{2}}\left(k\right)+B_{-\frac{1}{2}}\left(k\right)$

Order $\mathrm{\α}=\sqrt{\frac{{{\mathrm{Pl}}_0}^4}{{\mathrm{EI}}_1}}$

Then have:

$u\left(t\right)=A_1{J}_{-\frac{1}{2}}\left(\mathrm{\α}t\right)+B_{-\frac{1}{2}}\left(\mathrm{\α}t\right)---(2-2)$

From Bessel's function

$J_{-\frac{1}{2}}\left(\mathrm{\α}t\right)=\frac{cos\left(\mathrm{\α}t\right)}{\sqrt{(\mathrm{\π}/2)\mathrm{\α}t}}$

$Y_{-\frac{1}{2}}\left(\mathrm{\α}t\right)=\frac{sin\left(\mathrm{\α}t\right)}{\sqrt{(\mathrm{\π}/2)\mathrm{\α}t}}$

The solution of equation (1-3) is

$w=\frac{1}{t}\sqrt{\frac{2}{\mathrm{\π}\mathrm{\α}}}\[A_{1}cos\left(\mathrm{\α}t\right)+B_{1}sin\left(\mathrm{\α}t\right)\]$

That is:

$w=x\[Acos\left(\frac{\mathrm{\α}}{x}\right)+Bsin\left(\frac{\mathrm{\α}}{x}\right)\]---(2-3)$

Then have w differentiate:

$w^{\′}=\[Acos\left(\frac{\mathrm{\α}}{x}\right)+Bsin\left(\frac{\mathrm{\α}}{x}\right)\]+x\left(\frac{A\mathrm{\α}}{x^2}cos\frac{\mathrm{\α}}{x}-\frac{B\mathrm{\α}}{x^2}cos\frac{\mathrm{\α}}{x}\right)$

$w^{\′\′}=\frac{2A\mathrm{\α}}{x^2}cos\frac{\mathrm{\α}}{x}-\frac{2B\mathrm{\α}}{x^2}cos\frac{\mathrm{\α}}{x}+x\left(-\frac{A\mathrm{\α}}{x^4}cos\frac{\mathrm{\α}}{x}-\frac{2A\mathrm{\α}}{x^3}sin\frac{\mathrm{\α}}{x}+\frac{2\mathrm{\α}B}{x^3}cos\frac{\mathrm{\α}}{x}-\frac{{\mathrm{B\α}}^2}{x^4}\right)$

Can absorbing boundary equation be obtained by column with variable cross-sections top and bottom-hinged:

w(l ₀)＝0；w”(l ₀)＝0

w(l ₀+l)＝0；w”(l ₀+l)＝0

Buckling eigenvalue Theory Solution P can be obtained by last solution with reference to " Theoryofelasticstability " (TimoshenkoS.P. & GcrcJ.M.Theoryofelasticstability [M] .NewYork:McGraw-HillBookCompany.1961) _cr

$P_{cr}=\frac{{\mathrm{mEI}}_1}{l^2}$

Wherein, I ₁be column with variable cross-sections bottom surface moment of inertia, Coefficient m only and l ₀with l ₁ratio relevant, and need to obtain by solving transcendental equation.

1. consider the computational length coefficient μ of monolithic space action

1.1 computational length coefficient μ definitions

Based on theory of elasticity, according to aforementioned derivation, the critical bearing capacity N of Euler of the axial compression eigenvalue buckling of pin-ended taper column with variable cross-sections _cr0can be expressed as:

$N_{cr0}=K\frac{{\mathrm{EI}}_0}{L^2}---\left(1\right)$

I ₀for microcephaly's moment of inertia.Wherein COEFFICIENT K is that the expression formula of tapered pole moment of inertia I (x) provides.From formula (1), the same with uniform cross section Euler's formula post, the computational length of tapered pole and Euler's critical load N _crevolution between still meet square inverse relation.

In practice, because tapered post pillar two ends are not often desirable hinged constraint, when there is other constraint condition, compare with desirable hinged constraint, to have the computational length coefficient μ being not equal to 1, its axial compression Euler eigenvalue buckling bearing capacity can be expressed as:

$N_{cr}=K\frac{{\mathrm{EI}}_0}{{\left(\mathrm{\μ}L\right)}^2}---\left(2\right)$

If when two ends are constrained to hinged, formula (2) namely deteriorates to (1), i.e. the desirable μ of μ in formula ₀=1,

By formula (1) and formula (2) both sides phase, then can consider the computing formula of the computational length coefficient μ of monolithic space action:

$\mathrm{\μ}=\sqrt{\frac{N_{cr0}}{N_{cr}}}---\left(3\right)$

N _crpillar in the eigenwert of structure monolithic space action lower prop, N _cr0the eigenvalue buckling critical load of pillar under pin-ended constraint condition, μ is the computational length coefficient considering structure monolithic space action.

1.2 steps 1: the tapered pole eigenwert load N considering monolithic space action _cr

Consider the tapered pole eigenwert load N of monolithic space action _crcalculated by finite element software, its theory of computation is: theoretical according to existing Specification Design, and the stability bearing capacity impact of monolithic space action on pillar component comprises two aspects:

1, the effect of contraction that the beam be connected with styletable or roof grid structure rotate styletable:

2, the effect of contraction that in one-piece construction, other rod member coupled columns sides are moved: in specification " Code for design of steel structures GB50017 ", according to the overall lateral deformation stiffness of structure, the overall collapse form of pillar comprises without sidesway and side moves two kinds.Whether the anti-side such as enough supports, shear wall, cylindrical shell are set and move system.

For sideway structures system, in specification " Code for design of steel structures GB50017 " when concrete calculating other all pillar of this layer of supposition flexing all of also relatively safety, to ignore in integral structural system other pillars to the sidewise restraint of support column upper end.The computation sheet of side moves space behavior computational length coefficient is given in Appendix D.It calculates thinking and can be expressed as Fig. 2,3 and (Figure 2 shows that side moves multilayer multispan, suppose the corner equal and opposite in direction at the crossbeam two ends of same layer after buckling deformation, and the direction of corner is also identical during calculating; Fig. 3 simulates the computation model of single sway column, and this has, and the length of sway column is H, cross sectional moment of inertia is the right cylinder of I, and styletable is all subject to the constraint of bending resistance spring, and the constraint constant of upper end is r ₁, the constraint constant of lower end is r ₂), refer to document (Code for design of steel structures is understood and application, and Code for design of steel structures establishment group is write, Chinese Plan Press, 2003.11).

But only give in specification " Code for design of steel structures GB50017 " Appendix D the approximate treatment length factor that plane rule frame system considers space behavior.For large complicated space structure, the present invention is based on the thought that above-mentioned specification is same, comprehensive two factors above, in the overall space Deterministic Finite meta-model of large span Complicated Spatial Structure, discharge the sidesway constraint to calculating target pillar upper end, apply xial feed at styletable, overall Eigenvalue Buckling Analysis is carried out to structure, the eigenwert critical load N considering monolithic space action can be calculated _crand the buckling mode of correspondence.

Example: with reference to figure 4,5, for certain space structure, the buckling eigenvalue N of the side moves calculated by space block mold _crand the buckling mode of correspondence.(the marking in Fig. 4) that can try to achieve target post considers the eigenwert critical load N of monolithic space action _cr, unstability direction Y-direction N in Fig. 4 _cr=3.85x10 ⁸n.

1.3 steps 2: without the Eigenvalue Buckling Analysis N of the pin-ended post of space behavior _cr0

By setting up analysis model for finite element, the hinged target post in tapered pole two ends of pin-ended can be set up separately, and carry out Eigenvalue Buckling Analysis.Accurately can obtain the critical bearing capacity N of Euler of the axial compression eigenvalue buckling of the taper column with variable cross-sections of actual pin-ended _cr, avoid adopting the complicated theory of the carrying out of theoretical formula to solve.

Example: still for this pillar, the pin-ended tapered pole buckling eigenvalue N without space behavior can be tried to achieve by finite element software _cr0, without the buckling eigenvalue N of the pin-ended microcephaly column with constant cross sections of space behavior _cr0', Fig. 6 target post is without the pin-ended tapered pole buckling mode N of space behavior _cr0=4.392 × 10 ⁸the eigenvalue buckling mode N of N, Fig. 7 pin-ended microcephaly column with constant cross sections _cr0'=1.57 × 10 ⁸n.

1.4 steps 3: the computational length coefficient μ considering monolithic space action

By above-mentioned N _cr, N _cr0bring the calculation length of column coefficient μ that formula (3) can obtain considering structure monolithic space action into.

Example: still for this pillar:

$\mathrm{\μ}=\sqrt{\frac{N_{cr0}}{N_{cr}}}=\sqrt{\frac{4.392\×{10}^8}{3.85\×{10}^8}}=1.068$

1.4 steps 4: the concrete filled steel tube tapered pole computational length coefficient μ considering monolithic space action _eff

Get (EI) _eff=(EI) ₀i.e. little end section.Then in pin-ended situation, the equivalent calculated length coefficient of column with variable cross-sections

The computational length coefficient μ of comprehensive above-mentioned consideration monolithic space action tapered pole, and the small end uniform cross section equivalent calculated length coefficient μ of the hinged tapered pole of upper and lower side _eff0, so consider the equivalent calculated length coefficient μ of the tapered pole of monolithic space action _effcan be expressed as:

μ _eff＝μμ _eff0(4)

Example: still this post is example, considers the computational length coefficient μ of monolithic space action tapered pole, the small end uniform cross section equivalent calculated length coefficient μ of the hinged tapered pole of upper and lower side _eff0, so consider the computational length coefficient μ being equivalent to little end section of the tapered pole of monolithic space action _effcan be expressed as:

μ _eff＝μμ _eff0＝1.068×0.598＝0.639

The process flow diagram of above step 1 to 4, schematic diagram refer to accompanying drawing 9, Figure 10.

The press-bending stability bearing capacity of 2 concrete filled steel tube tapered poles is checked

Traditional approach can be adopted, by " concrete filled steel tube technical regulation: CECS28-2012 " standard, with the μ obtained _effthe press-bending stability bearing capacity of carrying out concrete filled steel tube tapered pole is checked.But this mode is comparatively loaded down with trivial details, the following method that can also the present inventor be adopted to propose further is checked, efficiency greatly improves: by structural unit one-piece construction finite element numerical simulation, obtain the post stability bearing capacity that concrete filled steel tube tapered pole considers monolithic space action, and computational analysis obtains the stability factor φ of the support column considering the overall effect of contraction in space, by the stability factor obtained the N-M ultimate bearing drawing target post is tried hard to, and substitutes into load case, the resistance to overturning of checking pillar.Ultimate bearing is tried hard to as accompanying drawing 8.

2.1 steel core concrete columns consider the coefficient of bearing caoacity reduction coefficient of overall space constraint

The stability Calculation formula of what " concrete filled steel tube technical regulation: CECS28-2012 " gave is uniform cross section steel pipe column.Therefore according to its 5.1.4 bar, uniform cross section concrete column considers the bearing capacity reducing coefficient of long thin impact for:

Work as L _eduring/D>4:

Work as L _eduring/D≤4:

D is the diameter of steel pipe; L _eeffective length for pillar:

L _e＝μ _effkL

L is the physical length of pillar.

K is the equivalent length coefficient considering shaft Bending moment distribution gradients affect, the second-order effects that the distortion under consideration pillar axle power under actual Moment causes, and is referred to as again the little P-δ effect that moment of flexure causes.Usually at norm of steel structure GB50017 and concrete specification GB50010 ^[50]the method that middle employing is revised moment of flexure, but have employed at CECS280-2012 this effect is considered to the method for computational length correction.

For frame with sidesway post

Work as e ₀/ r _cwhen≤0.8: k=1-0.625e ₀/ r _c

Work as e ₀/ r _cduring >0.8: k=0.5

In fact, k is directly related with the internal force of pillar, determined by the curvature under actual moment of flexure, and when two ends contrary sign is with under size moment of flexure, k value is 1 to the maximum.Due to very many during actual design checking computations operating mode.Therefore, for ease of intuitively checking the stressed of pillar accurately, judge intuitively, in this report, relatively conservative by k=1 value.

Therefore, the effective length L of pillar _e:

L _e＝μ _effkL(5)

2.2 consider that the concrete filled steel tube tapered pole compression-bending capacity of overall space constraint is checked

Have employed the M-N dependent equation consistent with the method for bearing capacity reduction pair coefficient and calculation and check is carried out to the compression-bending capacity of target pillar, and M-N dependent equation is provided by the interpretation of section of this specification provision 5.1.3 bar:

In formula, N, M are force value in end, M ₀for pure bending bearing capacity value:

M ₀＝0.4N ₀r _c(8)

R _cthe radius of core concrete; N ₀for axial compressive strength ultimate bearing force value:

$N_0=0.9A_c{f}_c(1+\sqrt{\mathrm{\θ}}+\mathrm{\θ})$

Wherein, θ is concrete filled steel tube confinement index

The N-M ultimate bearing drawing target post is tried hard to, and by the N under kind of Load Combination operating mode, M combination of internal forces is drawn together.Concrete drawing practice is as follows: (1) can try to achieve equivalent stability factor according to equivalent calculated length coefficient, equivalent stability factor is substituted into " concrete filled steel tube technical regulation: CECS28-2012 " 5.1.3 bar, 5.1.4 bar, thus draw out N-M ultimate bearing force curve; (2) in finite element software, calculate target post under each operating mode, styletable internal force situation, extract the data of its axle power N, moment M, data are drawn in N-M ultimate bearing force curve; (3) whether all comprise interior force according to N-M ultimate bearing force curve, differentiate target post whether unstability.

Example: still for this post, by above-mentioned " concrete filled steel tube technical regulation: CECS28-2012 " formula, the N-M ultimate bearing force curve of this pillar can be calculated.And and the pillar two ends that calculate of various Load Combination performance analysis N-M design load draw and together mark, can judge within the N-M ultimate bearing capacity envelope of curves that this pillar design load is in clearly, show that the cross section of this pillar meets designing requirement, and have suitable bearing capacity more than needed.Fig. 8 is post check result, M/ (φ in Fig. 8 ₁m ₀) namely the moment of flexure of post one end and the ratio of this newel post's yield moment be a characteristic, ordinate neither axial pressure but N/ (φ ₁n ₀)), the axial pressure of one end of post and the ratio of this end yield strength are also characteristics, φ ₁m ₀, φ ₁n ₀be the parameter of formula in specification " concrete filled steel tube technical regulation ", after pillar cross section is determined, both are constant, have asterisk in figure, the operating mode that small circle represents, are all tapered pole two ends with reference to specification to formula go out by respective Cross section calculation.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. consider concrete filled steel tube tapered pole Equivalent Calculation length and the calculation method for stability of monolithic space action, it is characterized in that step is:

(1) the concrete filled steel tube tapered pole eigenwert load N considering monolithic space action is calculated by finite element software _cr, without the Eigenvalue Buckling Analysis N of the pin-ended post of space behavior _cr0, and the buckling eigenvalue N of pin-ended microcephaly column with constant cross sections without space behavior _cr0';

(2) by following formula, the support column computational length coefficient μ considering the overall effect of contraction in space is tried to achieve:

$\mathrm{\μ}=\sqrt{\frac{N_{cr0}}{N_{cr}}};$

(3) the equivalent calculated length coefficient μ of concrete filled steel tube tapered pole under equivalent column with constant cross sections that two ends are hinged as follows, is drawn _eff0:

${\mathrm{\μ}}_{eff0}=\sqrt{\frac{{N_{cr0}}^{\′}}{N_{cr0}}};$

(4) the equivalent calculated length coefficient μ that tapered pole considers monolithic space action as follows, is obtained _eff:

μ _eff＝μμ _eff0；

(5) by " concrete filled steel tube technical regulation: CECS28-2012 " regulation, the tapered pole above-mentioned derivation drawn considers the equivalent calculated length coefficient μ of monolithic space action _effsubstitute into 5.1.3 bar, 5.1.4 bar, the press-bending stability bearing capacity of carrying out concrete filled steel tube tapered pole is checked.

2. concrete filled steel tube tapered pole Equivalent Calculation length and the calculation method for stability considering monolithic space action as claimed in claim 1, it is characterized in that: step (1) is specially, consider space behavior, block mold is set up in finite element software, again by the target post emission levels constraint in model, go out with the buckling analysis function calculating of software the eigenwert load N that target post concrete filled steel tube tapered pole considers monolithic space action _cr, then use the Eigenvalue Buckling Analysis N of the hinged concrete filled steel tube tapered pole in the single two ends of buckling analysis functional analysis _cr0, in like manner analyze the buckling eigenvalue N of the pin-ended microcephaly column with constant cross sections without space behavior _cr0'.