CN101030231A - Method for determining non-destructive vertical light-steel construction bearing ability - Google Patents

Abstract

A nondestructive method for confirming load-carry ability of high light steel structure includes applying free vibration test to actually test out two types of axial forces and corresponding basic inherent frequency of said structure, setting up linear relation formula of basic inherent to axial force based on actual test result and using set-up linear relation formula to solve out axial load when basic inherent frequency is zero for obtaining buckling load of said structure so as to confirm out load-carry ability of said structure.

Description

Non-destructive vertical light-steel construction bearing ability is determined method

Technical field

The present invention relates to a kind of definite method of towering lightweight steel construction bearing capacity, is example with towering derrick geometry, has provided a kind of bearing capacity based on non-destructive testing (NDT) and has determined method.

Background technology

So the derrick geometry in the towering steel construction widespread use petroleum industry, the fields such as fast power transformation pylon of power industry, the determining of its bearing capacity for carrying out engineering design and guaranteeing that engineering safety is significant.Yet up to now, the determining of towering lightweight steel construction bearing capacity both not have the computing formula that is suitable for, do not have the method for testing of science yet, can not adopt destructive test again, therefore was a difficult problem of needs solution for a long time always.

Summary of the invention

The technical problem to be solved in the present invention is: deduce by theoretical analysis and formula, propose a kind of method that towering lightweight steel construction bearing capacity just can be more accurately determined in destructive test that need not.

In order to solve above technical matters, relevant issues have been carried out following theoretical analysis to the applicant and formula is deduced:

1 utilization is stablized the power criterion and is set up equation

At first analyze when giving a certain small sample perturbations and the motion of the system that causes for initial equilibrium conditions.

Imagination has that a lower end is fixed, the flexible freely vertically lath (referring to Fig. 1) in upper end.Suppose that the effect of lath upper end has pressure P (not considering the quality of lath) straight down.When acting force was less, lath kept rectilinear form with pressurized.If make the lath upper end depart from original position (applying microvibration) a little, loosen then, then lath will be swung near vertical position.If the caused moving displacement of microvibration remains in certain scope, then original state is stable.Promptly under steady state (SS), for the motion that system takes place small sample perturbations, position of each point is with the unlikely scope of regulation in advance that surpasses on it.If what discussed is conservative system, its constraint reaction and resistance institute work all equal zero.Such system will be done proper vibration (among Fig. 1 shown in the dotted line) in former balance position.The frequency of swing will be different with the size of pressure.When pressure increases, frequency will reduce; When pressure reaches a certain critical value, the frequency of small sway will level off to zero.Rod member will be in the indifferent equilibrium state this moment.In this case, stability criterion is converted into the natural frequency of vibration and equals zero.Here it is research stability of equilibrium the power criterion.Usually can carry out according to the following step: the then small free vibration of early work in the equilibrium position of being discussed for a certain reason of (1) supposition system, write out vibration equation, and obtain the expression formula of its vibration frequency; Frequency this condition that equals zero is determined critical load when (2) being in critical conditions according to system.

The central compression rod member that two ends shown in Figure 2 are hinged, the differential equation of its deformation curve is

$\mathrm{EI}\frac{d^{4}v}{{\mathrm{dx}}^4}+P\frac{d^2\mathrm{<figure-callout\; id="2"\; label="v\; dx"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">v</figure-callout>}}{{\mathrm{dx}}^{}}=+q---\left(1\right)$

In the formula, q is the lateral load intensity.Use d'Alembert principle, adopt the inertial force of the long quality of unit bar as the lateral load intensity, promptly $-q=\stackrel{\&OverBar;}{m}\frac{{\&PartialD;}^{2}v}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">t</figure-callout>}}^2},$ Former that its differential equation of motion is

$\mathrm{EI}\frac{{\&PartialD;}^{4}v}{\&PartialD;x^4}+P\frac{{\&PartialD;}^{2}v}{{\&PartialD;x}^2}+\stackrel{\&OverBar;}{m}\frac{{\&PartialD;}^{2}v}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=0---\left(2\right)$

In the formula, EI is the bendind rigidity of rod member, and m is the quality of rod member unit length; (x t) is the amount of deflection of rod member to v=v, and it is not only the function of coordinate x, but also is the function of time t.

Following formula can be write as

$\frac{{\&PartialD;}^{4}v}{\&PartialD;x^4}+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\frac{{\&PartialD;}^{2}v}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}+\frac{\stackrel{\&OverBar;}{m}}{\mathrm{EI}}\frac{{\&PartialD;}^{2}v}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=0---\left(3\right)$

Wherein k is a parameter.

Make v (x, t)=X (x) T (t), with its substitution formula (3),

$T\frac{d^{4}X}{{\mathrm{dx}}^4}+k^{2}T\frac{d^2\mathrm{<figure-callout\; id="2"\; label="X\; dx"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">X</figure-callout>}}{{\mathrm{dx}}^{}}=-\frac{\stackrel{\&OverBar;}{m}}{\mathrm{EI}}X\frac{d^{2}T}{{\mathrm{dt}}^2}---\left(4\right)$

The left side of this equation only changes with x, and the right is only relevant with t.So equation has only when left and right two parts are equal to same constant and can set up.Make that this constant is a, then have

$-\frac{\stackrel{\&OverBar;}{m}}{\mathrm{EI}}\frac{1}{T}\frac{d^2\mathrm{<figure-callout\; id="2"\; label="T\; dt"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">T</figure-callout>}}{{\mathrm{dt}}^{}}=a---\left(5\right)$

Formula (5) is rewritten into following form

$\frac{d^2\mathrm{<figure-callout\; id="2"\; label="T\; dt"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">T</figure-callout>}}{{\mathrm{dt}}^{}}+\frac{\mathrm{EI}}{\stackrel{\&OverBar;}{m}}\mathrm{\&alpha;T}=0---\left(6\right)$

Its separate into

T＝A ₁cosωt+B ₁sinωt (7)

In the formula

${\mathrm{\&omega;}}^2=\frac{\mathrm{EI}}{m}\mathrm{\&alpha;}---\left(8\right)$

And ω is exactly the natural frequency of depression bar.

Determine the expression formula of a below.For this reason, formula (5) is rewritten as

$\frac{d^{4}X}{{\mathrm{dx}}^4}+k^2\frac{d^{2}X}{{\mathrm{dx}}^2}-\mathrm{aX}=0---\left(9\right)$

Corresponding secular equation is

s ⁴+k ²s ²-a＝0 (10)

This equation has two real roots and two imaginary roots.Quotation mark

${\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="A20071002132800124.png,A20071002132800126.png"\; state="\{\{state\}\}">s</figure-callout>}}_1^2=\frac{\sqrt{k^4+4\mathrm{\&alpha;}}-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}{2},{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">s</figure-callout>}}_2^2=\frac{\sqrt{k^4+4\mathrm{\&alpha;}}+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}{2}$

Can write out equation (9) separate for

X(x)＝Achs ₁t+Bshs ₁x+Ccoss ₂x+Dsins ₂x (11)

Utilize the boundary condition of hinged depression bar, i.e. x=0,1 o'clock, $v=\frac{d^2\mathrm{<figure-callout\; id="2"\; label="v\; dx"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">v</figure-callout>}}{{\mathrm{dx}}^{}}=0,$ Provide A=C=B=0, Dsins ₂L=0 notices D ≠ 0 (not being in the straight line equilibrium state otherwise vibration does not take place rod member),

${\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">s</figure-callout>}}_2=\frac{\mathrm{n\&pi;}}{l}(n=\mathrm{1,2,3}......)---\left(12\right)$

{。##.##1},

${\mathrm{\&alpha;}}_n=\frac{n^4{\mathrm{\&pi;}}^4}{l^4}(1-\frac{k^2{l}^2}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&pi;}}^2})---\left(13\right)$

With its substitution formula (8), can get n rank vibration frequency

${\mathrm{\&omega;}}_n={\mathrm{\&omega;}}_{0n}{(1-\frac{{\mathrm{Pl}}^2}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&pi;}}^2\mathrm{EI}})}^{1/2}---\left(14\right)$

In the formula

${\mathrm{\&omega;}}_{0n}=\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&pi;}}^2}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">l</figure-callout>}}^2}\sqrt{\frac{\mathrm{EI}}{\stackrel{\&OverBar;}{m}}}---\left(15\right)$

It is that the hinged rod member in two ends is not having pressure P to make the n rank natural vibration frequency of time spent.

By formula (14) as can be known, the null condition of system n rank vibration frequency is

$\frac{{\mathrm{Pl}}^2}{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&pi;}}^2\mathrm{EI}}=1$

Can try to achieve critical load in view of the above is

$P=\frac{{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&pi;}}^2\mathrm{EI}}{l^2}---\left(16\right)$

The minimum value of its critical load is

$P_E=\frac{{\mathrm{\&pi;}}^2\mathrm{<figure-callout\; id="2"\; label="EI\; l"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">EI</figure-callout>}}{l^{}}$

Fig. 3 has provided the approximation relation (linking to each other with straight line approx between A, the B) between frequency and the pressure.

2, utilize theory of structural dynamics to set up equation

One cantilever design bending stiffness is EI, and linear mass is m.Bear a constant vertical load on its top.Its deflection profile is assumed to when free vibration:

$\mathrm{\&Psi;}\left(x\right)=1-\cos \frac{\mathrm{\&pi;x}}{2l}---\left(17\right)$

Then Yun Dong amplitude is expressed with generalized coordinate z (t)

v(x，t)＝Ψ(x)z(t) (18)

Employing Hamilton principle is set up system's Free Vibration Equations and is

$m^{*}\stackrel{\&CenterDot;\&CenterDot;}{z}\left(t\right)+{\stackrel{\&OverBar;}{k}}^{*}z\left(t\right)=0---\left(19\right)$

Wherein:

Generalized mass:

$m^{*}={\&Integral;}_0^l\stackrel{\&OverBar;}{m}{\mathrm{\&Psi;}}^2\left(x\right)\mathrm{dx}=0.228\stackrel{\&OverBar;}{m}l---\left(20\right)$

Broad sense rigidity $k^{*}={\&Integral;}_0^l\mathrm{EI}{\left({\mathrm{\&Psi;}}^{\&prime;\&prime;}\left(x\right)\right)}^2\mathrm{dx}=\frac{{\mathrm{\&pi;}}^4}{32}\frac{\mathrm{EI}}{l^3}---\left(21\right)$

The broad sense geometric stiffness $k_G^{*}={\&Integral;}_0^{l}N{\left({\mathrm{\&Psi;}}^{\&prime;}\left(x\right)\right)}^2\mathrm{dx}=\frac{{\mathrm{N\&pi;}}^2}{8l}---\left(22\right)$

Associating broad sense rigidity ${\stackrel{\&OverBar;}{k}}^{*}=k^{*}-k_G^{*}=\frac{{\mathrm{\&pi;}}^4}{32}\frac{\mathrm{EI}}{l^3}-\frac{N{\mathrm{\&pi;}}^2}{8l}---\left(23\right)$

Therefore, the equation of motion of consideration axial force effect is

$0.228\stackrel{\&OverBar;}{m}l\stackrel{\&CenterDot;\&CenterDot;}{z}\left(t\right)+\frac{{\mathrm{\&pi;}}^4\mathrm{EI}}{32l^3}(1-\frac{N}{\frac{{\mathrm{\&pi;}}^2\mathrm{EI}}{{4l}^2}})z\left(t\right)=0---\left(24\right)$

The basic natural frequency of system is

${\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="A20071002132800124.png,A20071002132800125.png"\; state="\{\{state\}\}">l</figure-callout>}}^2=\frac{{\mathrm{\&pi;}}^4\mathrm{EI}}{32\&times;0.228m{l}^4}(1-\frac{N}{\frac{{\mathrm{\&pi;}}^2\mathrm{EI}}{4l^2}})$

$=13.2\frac{\mathrm{EI}}{m{l}^4}(1-\frac{N}{\frac{{\mathrm{\&pi;}}^2\mathrm{EI}}{{4l}^2}})---\left(25\right)$

By equation (25) as can be known, the basic natural frequency ω of cantilever design ₁ ²Linear with its vertical axial force of being born.For other version, can adopt similar method to prove above-mentioned conclusion establishment.

Formula (25) has provided the basic natural frequency ω of structure ₁ ²Linear with its axial force N that is born, mensuration or calculating that this has proved the basic natural frequency under different xial feeds can be used in the flexing load that comes predict in the non-destructive testing (NDT).

Deduce based on above theoretical analysis and formula, the present invention determines that the method for towering lightweight steel construction bearing capacity can be summed up as following steps:

1), surveys under two kinds of axial force situations the basic natural frequency of towering lightweight steel construction correspondence at least with the free vibration test;

2), set up the linear relation of basic natural frequency and axial force at least with the basic natural frequency measured data end value of the specific axial force correspondence of two groups;

3), according to building linear relation, the xial feed of correspondence when obtaining basic natural frequency and be zero obtains the flexing load of towering lightweight steel construction, thereby determines the bearing capacity of towering lightweight steel construction.

Above step 1) can be surveyed the basic natural frequency ω of towering lightweight steel construction of no axial force earlier with the free vibration test ₁₀ ²Apply actual measurement behind the axial force N again to the basic natural frequency ω of towering lightweight steel construction that should axial force ₁₁ ²

In order to improve the precision of determining the result, every group of data of above free vibration test procedure can be after at least twice identical actual measurement, the value as a result of of averaging.In addition, when using the basic natural frequency that adds under the two or more axial force situations of axial force free vibration test actual measurement, can adopt several different axial force N values, survey respectively the basic natural frequency of towering lightweight steel construction that should axial force, the basic natural frequency mean value that calculates different axial force mean value correspondences again is as one group of measured data.

Afterwards, can further check by Computer Simulation.At first by the Drilling derrick dynamic characteristic equation that bears vertical load

|[K]-λ _g[K _g]-ω ²[M]|＝0 (26)

In the formula, [K], [K _g], [M] be respectively stiffness matrix, geometric stiffness matrix, mass matrix behind the derrick finite element discretization.

In the practicality, can calculate, obtain the pairing basic frequency of loads at different levels respectively towering lightweight steel construction hierarchical loading.By Computer Simulation obtain the derrick geometry basic frequency with and the relation of the axial force N that born, from (26) formula as can be seen, when ${\mathrm{\&omega;}}_1^2=0$ The time, the generalized eigenvalue of asking is the flexing load of the Drilling derrick of asking.

Concrete check analysis situation is as follows:

Cantilever design shown in Figure 4 is established EI, m is constant.

Adopt finite element method to disperse, be divided into 3 unit altogether, hierarchical loading adopts formula (26) to calculate basic frequency ω ₁ ²Concern as shown in Figure 4 with the axial force N that is born.As can be seen from Figure 4, when ${\mathrm{\&omega;}}_1^2=0,$ Pairing xial feed is the flexing load N that asks _Or

$N_{\mathrm{or}}=2.44\frac{\mathrm{EI}}{l^2}---\left(27\right)$

The theoretical solution of this cantilever design flexing load is

$P_{\mathrm{or}}=\frac{{\mathrm{\&pi;}}^2}{4}\frac{\mathrm{EI}}{l^2}---\left(28\right)$

Contrast (27) and (28) formula, both result of calculation is approaching, and the error of calculation is 1.1%.

Plane frame structure shown in Figure 5 is established EI, m, the long L of bar is constant.Adopt finite element method to disperse, each bar is divided into 2 unit, to this plane framework hierarchical loading, adopts formula (26) to calculate basic frequency ω ₁ ²Concern as shown in Figure 6 with bearing axial force N, by ω among Fig. 6 ₁ ²The extrapolation of-N relation is worked as ${\mathrm{\&omega;}}_1^2=0$ The time pairing vertical load N be the flexing load N that asks _Or

$N_{\mathrm{or}}=7.40\frac{\mathrm{EI}}{L^2}---\left(29\right)$

The theoretical solution of this planar structure flexing load is

$P_{\mathrm{or}}=7.34\frac{\mathrm{EI}}{l^2}---\left(30\right)$

Contrast (29) and (30) formula, both result of calculation is approaching, and the error of calculation is 0.8%.This shows that definite result of the present invention and theoretical solution are approaching, thereby proof the inventive method is correct, credible result can be applied to engineering practice fully.

Description of drawings

The present invention is further illustrated below in conjunction with accompanying drawing.

Fig. 1 is flexible vertically lath synoptic diagram.

Fig. 2 is the central compression rod schematic representation.

Fig. 3 is natural frequency of vibration ω ²Graph of a relation with pressure N.

Fig. 4 is the natural frequency of vibration ω of cantilever design ²With pressure N graph of a relation.

Fig. 5 is from plane framed structure synoptic diagram.

Fig. 6 is plane frame structure natural frequency of vibration ω ²With pressure N graph of a relation.

Fig. 7 is an one embodiment of the invention bearing capacity Drilling derrick structural drawing to be determined.

Fig. 8 is Drilling derrick natural frequency of vibration ω among Fig. 7 _i ²With pressure N _iGraph of a relation.

Embodiment

Embodiment one

Present embodiment is determined with JJ300/43-A type Drilling derrick bearing capacity shown in Figure 7, is specified towering lightweight steel construction bearing capacity and determine method.

At first survey the basic natural frequency of Drilling derrick of no axial force with the free vibration test ${\mathrm{\&omega;}}_{10}^2=25.5;$ After then applying an axial force N=1000kN again, actual measurement is to the basic natural frequency of towering lightweight steel construction that should axial force ${\mathrm{\&omega;}}_{11}^2=19.6.$

Afterwards, set up basic natural frequency ω with two groups of measured datas ₁ ²With the linear relation of axial force N, can obtain: $\frac{{\mathrm{\&omega;}}_1^2-25.5}{19.6-25.5}=\frac{N-0}{1000-0}$

Become after the simplification: ${\mathrm{\&omega;}}_1^2=25.5-0.00585N;$

Last according to linear relationship shown in Figure 8, obtaining basic natural frequency is zero ${\mathrm{\&omega;}}_1^2=0$ The time pairing xial feed, promptly obtain the flexing load P of towering lightweight steel construction _Or=4350KN, thereby the bearing capacity of definite Fig. 7 Drilling derrick structure.

Further check with Computer Simulation, the result is very identical.Therefore, definite method of present embodiment Drilling derrick flexing load carrying is definite very practical to Drilling derrick flexing load, need not destructive test and can obtain quantized result, and can combine with Computer Simulation, thus a new road of having opened up assessment derrick bearing capacity.Obviously, this method also is applicable to determining of the maximum unstability load of the towering lightweight steel construction of other engineering.

Present embodiment need not to carry out destructive test, by simple and direct step, just can draw the Drilling derrick structure bearing capacity structure with enough engineering accuracys, thereby solve an insurmountable for a long time difficult problem.

In addition to the implementation, the present invention can also have other embodiments.All employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop on the protection domain of requirement of the present invention.

Claims (5)

1. a non-destructive vertical light-steel construction bearing ability is determined method, may further comprise the steps:

1), surveys under two kinds of axial force situations the basic natural frequency of towering lightweight steel construction correspondence at least with the free vibration test;

2), set up the linear relation of basic natural frequency and axial force at least with the measured data end value of the corresponding basic natural frequency of the specific axial force of two groups;

3), according to building linear relation, the xial feed of correspondence when obtaining basic natural frequency and be zero obtains the flexing load of towering lightweight steel construction, thereby determines the bearing capacity of towering lightweight steel construction.

2. determine method according to the described towering lightweight steel construction bearing capacity of claim 1, it is characterized in that: described step 1) is surveyed the basic natural frequency of towering lightweight steel construction of no axial force earlier with the free vibration test; Apply actual measurement after the axial force again to the basic natural frequency of towering lightweight steel construction that should axial force.

3. determine method according to the described towering lightweight steel construction bearing capacity of claim 2, it is characterized in that: every group of free vibration test for data after at least twice identical actual measurement, the value as a result of of averaging.

4. determine method according to claim 2 or 3 described towering lightweight steel construction bearing capacities, it is characterized in that: after adding the basic natural frequency under the two or more axial force situations of axial force free vibration test actual measurement, with the basic natural frequency mean value of each axial force mean value correspondence as the measured data end value.

5. determine method according to the described towering lightweight steel construction bearing capacity of claim 4, it is characterized in that: check bearing capacity by Computer Simulation.

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