CN105223272B - A kind of method and quality vibrator of quick test Hollow Slab Beam Bridge Transverse Distribution - Google Patents

A kind of method and quality vibrator of quick test Hollow Slab Beam Bridge Transverse Distribution Download PDF

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CN105223272B
CN105223272B CN201510615159.9A CN201510615159A CN105223272B CN 105223272 B CN105223272 B CN 105223272B CN 201510615159 A CN201510615159 A CN 201510615159A CN 105223272 B CN105223272 B CN 105223272B
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CN105223272A (en
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汪志昊
周佳贞
徐宙元
李文礼
李宁
李晓克
黄来科
范永钢
侯起阳
熊坤
谭雅
汪志华
刘鑫鑫
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North China University of Water Resources and Electric Power
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Abstract

The invention belongs to engineering structure detection technique field, and in particular to the method and quality vibrator, this method of a kind of quick test set-up formula prefabricated concrete hollow slab girder bridge Transverse Distribution include:Each hollow slab girder vibration frequency average value f is calculated;It is determined that the vertical exciting quality of the inertia mass vibrator installed in jth beam:Vibrator is measured with frequency fj, amplitude A stable state exciting when each beam vertical motion speed time-domain signal;Determine the dynamic deflection maximum y of each girder span middle sectionij;Calculate the Transverse Distribution η of No. i-th beam under exciting effect in j girder spansij.The present invention is loaded using single-point, influencing each other when avoiding multipoint excitation, has the advantages of accurate, quick and economic;Load mode switchs to power loading by static loading, due to clear and definite corresponding relation between maximum dynamic deflection and natural bow be present, test result of the present invention is with theoretical method more closely, measurement is not limited by under-clearance, test process is simple, quick, is easy to quickly resume traffic.

Description

A kind of method and quality vibrator of quick test Hollow Slab Beam Bridge Transverse Distribution
Technical field
The invention belongs to engineering structure detection technique field, and in particular to a kind of quick test set-up formula prestressed concrete The method and quality vibrator of Hollow Slab Beam Bridge Transverse Distribution.
Background technology
When the essence of bridge lateral breadth coefficient is that unit force acts on certain piece girder span middle section, what each beam undertook respectively The size of power, it has reacted the lateral ties between each beam, aids in determining whether the least favorable load arrangement of bridge.In highway bridge In beam design, generally extension is calculated as the multiple that the peak load that certain root girder is undertaken is each axle weight.In packaged type bridges In the detecting appraisal of structure, the measure of Transverse Distribution is also a highly important job.
In existing Bridge Design specification, prefabricated PC concrete hollow slab girder bridge is typically calculated using transversely hinge The Transverse Distribution of spaning middle section.This method, which assumes only to transmit in bonding crack (hinge seam) under vertical uniform load q, vertically cuts Power, the concentrated force P that will act on span centre are equivalent to half-wave sine load(loading characteristic meets former after equivalent The boundary condition of stressing conditions, and equivalent forward and backward mid-span deflection is sufficiently close to), solve to obtain the span centre of each beam by force method Amount of deflection.During actual calculating, the cross section property of hollow slab girder is calculated first, then directly according to stiffness parameters(wherein, I represents section bending resistance the moment of inertia, ITSection torsional moment inertia is represented, b represents the width of every beam, L represents to calculate across footpath), looking into articulated slab load relieving system influences the perpendicular mark table of line, calculates Transverse Distribution.
The Transverse Distribution detection of prefabricated PC concrete hollow slab girder spanning middle section, is all based on loaded vehicle and adds The method measure of load.I.e.:Loaded vehicle is carried on span centre most unfavorable combination, measures the mid-span deflection of each beam, and with single The amount of deflection divided by combined deflection of beam obtain Transverse Distribution.
Obviously, theoretical computational methods clear principle, definite conception.But actual measuring method but has with theoretical method Very big discrepancy.Actually more to be loaded using loaded vehicle in load arrangement, load action is and theoretical on multiple points of multi-disc beam On should be single-point span centre loading;On Method And Principle, the reflection of the Transverse Distribution of bridge is transverse direction between each beam Contact, and bridge is integrally a space structure, single-point is loaded with beneficial to the contact accurately analyzed between each beam, in bridge The local damage of the problem of being also easier to find lateral connection during detection, i.e. positioning hinge seam.And in the case of multipoint excitation, respectively Influenced each other between load(ing) point, measured amount of deflection is different from theoretical method, and surveys only as under the effect of multiple concentrated forces It is superimposed amount of deflection, it is difficult to identify the lateral connection disease of bridge.In addition, in practical operation, loaded vehicle is got out before measurement, Support, installation displacement meter etc. are set up under bridge, workload is big, wastes time and energy, and uneconomical.
The content of the invention
The present invention for existing measuring method differs larger with theoretical method, time and effort consuming during measure, and cost is larger etc. asks Topic, propose a kind of quick method and quality vibrator for surveying Hollow Slab Beam Bridge Transverse Distribution.The technical scheme is that: A kind of method of quick test Hollow Slab Beam Bridge Transverse Distribution, this method comprise the following steps:
Step 1 tests to obtain the vertical intrinsic frequency f of single order of each hollow slab girder using ambient vibration advocate approach1、 f2……fnWith damping ratios ζ1、ζ2……ζn, wherein n is hollow sheet number, and average frequency value f is calculated;
Step 2: according to the requirement of hollow slab girder maximum defluxion limit value, it is determined that the inertia mass exciting installed in jth beam The vertical exciting quality of device:
In formula:
mShakeThe moving-mass of vibrator is represented,
ζjThe damping ratios of jth beam are represented,
MjThe gross mass of jth beam is represented,
L represents the calculating across footpath of beam,
A represents the displacement amplitude of vibrator,
ηjRepresent that the spaning middle section Transverse Distribution of jth beam (unit force is acted in jth girder span simultaneously) is theoretical Calculated value;
Step 3: inertia mass vibrator is installed above the span centre of jth beam, the position installation fixation in each girder span Low frequency vibration pickup, vibrator is measured with vibration frequency fj, amplitude A stable state exciting when each beam span centre vertical motion speed time domain Signal;
Step 4: determine the dynamic deflection maximum y of each girder span middle sectionij:Rate signal is integrated to obtain in frequency domain The dynamic deflection curve of displacement signal, i.e. bridge, the average of the crest of maximum and the absolute value of trough is taken on dynamic deflection curve, made For the maximum dynamic deflection value y of No. i-th girder span middle section under the exciting effect in j girder spansij
Step 5: calculate the spaning middle section Transverse Distribution η of No. i-th beam under exciting effect in j girder spansij
A kind of inertia mass vibrator of quick test Hollow Slab Beam Bridge Transverse Distribution, including:Bottom plate, guide shaft and matter Gauge block, guide shaft are cylinder, are fixedly connected at bottom plate center, and fixing hole and column, the upper surface of column are provided with bottom plate Caging bolt is installed, helical compression spring, helical compression spring upper-end contact mass are set with guide shaft, mass passes through linear bearing It is connected with guide shaft, limiting plate is provided with by screw thread on the top of guide shaft.
The inertia mass vibrator of described quick test Hollow Slab Beam Bridge Transverse Distribution, bottom plate pass through chemical bolt It is anchored on hollow slab girder.
The inertia mass vibrator of described quick test Hollow Slab Beam Bridge Transverse Distribution, the vibration frequency of vibrator It is adjusted by the quality for increasing and decreasing mass.
The inertia mass vibrator of described quick test Hollow Slab Beam Bridge Transverse Distribution, the mass to top The distance of limiting plate and lowermost limit bolt is equal.
The beneficial effects of the invention are as follows:1st, accurate, than existing automobile Loading Method, the invention is loaded using single-point, kept away Influencing each other when having exempted from multipoint excitation;Load mode switchs to power loading by static loading, due to maximum dynamic deflection and quiet scratches Clear and definite corresponding relation between degree be present, test result of the present invention and theoretical method are more close.
2nd, quick, this method is in measurement process without proping arrangement displacement meter, required vibrator and pick-up under bridge Device is arranged on bridge floor, and measurement is not limited by under-clearance;Test process is simple, quick, is easy to quickly resume traffic.
3rd, economical, the invention only needs to install vibrator and vibration pickup in bridge floor in measurement process, it is not necessary to which loaded vehicle adds Carry, without the proping arrangement displacement meter under bridge, test process is simple, reduces the spending manually with apparatus, time saving and energy saving, Saving fund.
Brief description of the drawings
Fig. 1 is the flow chart of the quick measure bridge lateral breadth coefficient method of the present invention;
Fig. 2 is the structural representation of vibrator of the present invention;
In figure, 1, limiting plate, 2, circular mass, 3, bolt, 4, column, 5, chemical bolt, 6, linear bearing, 7, spiral Stage clip, 8, guide shaft, 9, bottom plate, 10, hollow slab girder.
Embodiment
Embodiment 1:With reference to Fig. 1-Fig. 2, one kind of prefabricated PC concrete hollow slab girder bridge Transverse Distribution is fast Fast method of testing, its central principle are to replace traditional loaded vehicle static loading using less dynamic load stable state exciting, are passed through Test obtained hollow slab girder spaning middle section maximum dynamic deflection inverse and go out maximum static deflection, finally further according to the cross direction profiles of classics Coefficient formulas obtains Transverse Distribution.
This method comprises the following steps:
Step 1: test to obtain the vertical intrinsic frequency f of single order of each hollow slab girder using ambient vibration advocate approach1、 f2……fnWith damping ratios ζ1、ζ2……ζn, average frequency value f is calculated;
Step 2: according to the requirement of hollow slab girder maximum defluxion limit value, it is determined that the inertia mass exciting installed in jth beam The vertical exciting quality of device:
In formula:
mShakeThe moving-mass of vibrator is represented,
ζjThe damping ratios of jth beam are represented,
MjThe gross mass of jth beam is represented,
L represents the calculating across footpath of beam,
A represents the displacement amplitude of vibrator,
ηjRepresent that the spaning middle section Transverse Distribution of jth beam (unit force is acted in jth girder span simultaneously) is theoretical Calculated value.
Step 3: the fixed inertia mass vibrator of top installation in jth girder span, position installation is solid in each girder span Determine low frequency vibration pickup, measure vibrator with frequency fj, amplitude A stable state exciting when each beam span centre vertical motion speed time domain letter Number.
Step 4: determine the dynamic deflection maximum y of each girder span middle sectionij:Rate signal is integrated to obtain in frequency domain The dynamic deflection curve of displacement signal, i.e. bridge, the average of the crest of maximum and the absolute value of trough is taken on dynamic deflection curve, made For the maximum dynamic deflection value y of No. i-th girder span middle section under the exciting effect in j girder spansij
Step 5: calculate the spaning middle section Transverse Distribution η of No. i-th beam under exciting effect in j girder spansij
A kind of inertia mass vibrator of quick test Hollow Slab Beam Bridge Transverse Distribution, including, bottom plate, guide shaft and matter Gauge block, guide shaft are cylinder, are fixedly connected at bottom plate center, and fixing hole and column, the upper surface of column are provided with bottom plate Caging bolt is installed, helical compression spring, helical compression spring upper-end contact mass are set with guide shaft, mass passes through linear bearing It is connected with guide shaft, limiting plate is provided with by screw thread on the top of guide shaft.
Bottom plate is anchored on hollow slab girder by chemical bolt, and the frequency of vibrator is carried out by increasing and decreasing the quality of mass Regulation, the distance of the mass to uppermost limit plate and lowermost limit bolt are equal.
Wherein, classical Transverse Distribution calculation formula is when unit force acts on position in j girder spans, in each girder span Natural bow be designated as ust.Then the Transverse Distribution of No. i-th girder span middle section is:
The Transverse Distribution of dynamic action underbeam calculates
1. the modal mass of hollow slab girder single-degree of freedom vibration model:
Take:
It can obtain:
M=0.5M
2. differential equation of motion of the hollow slab girder one degree of freedom modeling under the effect of extraneous Simple Harmonic Load
Primary condition:
In formula:C=2m ω ζ;
M represents modal mass, and ζ represents damping ratio, and ω represents exciting circular frequency, ωnRepresent the inherent circular frequency of beam, P0Table Show exciting force.
Gained knowledge, can obtained by mathematical computations and structural dynamic:
In formula:
ucRepresent transient response;
upRepresent homeostatic reaction;
Represent beam in static(al) p0Amount of deflection under effect;
ζ represents the damping ratios of beam;
Represent the damping vibrition circular frequency of beam;
ωnRepresent the non-damping vibration circular frequency of beam;
ω represents exciting circular frequency.
The present invention carries out the calculating of Transverse Distribution using the amplitude under homeostatic reaction.
Homeostatic reaction is only considered below:
ut=Csin ω t+D cos ω t
Amplitude can be obtained by mathematical computations
In formula:
F represents excited frequency;
fiRepresent the intrinsic frequency of i beams.
When exciting force acts on j beams with frequency f, both form resonance.Due to the lateral ties of each beam, every beam is all Acted on by frequency f exciting force.The steady-state amplitude y of No. i-th beamijFor:
In formula:usiRepresent the natural bow of No. i-th beam.
Then:
When power acts on j beams, the spaning middle section Transverse Distribution of No. i-th beam is:
Particularly, if the natural frequency of vibration and damping ratio of each beam are equal, above formula is reduced to:
Obviously, when each beam natural frequency of vibration is equal, the ratio between its spaning middle section Transverse Distribution is equal to each beam steady-state amplitude The ratio between.
Inertia mass vibrator design procedure
1. design excited frequency:In order to reach the effect of resonance, excited frequency should take equal with each beam natural frequency of vibration.It is actual The difference very little of each beam of bridge, intrinsic frequency is of substantially equal, and a large amount of detection examples also demonstrate this point.On this basis, The present invention takes the average value of each girder natural frequency of vibration as the excited frequency f of vibrator.
2. design exciting quality:According to《Highway reinforced concrete and prestressed concrete bridge contain design specification》Regulation, steel Reinforced concrete and prestressed concrete beam bridge span centre maximum defluxion must not exceed L/600.
Calculated and known by the spaning middle section Transverse Distribution of dynamic action underbeam:
Then:
Above formula indicates the corresponding relation of the amount of deflection under Static behavior and the amplitude under dynamic action, i.e. dynamic magnification factor It is relevant with excited frequency, the natural frequency of vibration and damping ratio.
In the bridge machinery of reality, the intrinsic frequency of each beam can be measured, makes excited frequency be equal to intrinsic frequency, i.e., F=fi
For inertia mass vibrator:
P0=kShakeA=4mShakeπ2f2A
In formula, A represents amplitude.
For the jth beam of inertia mass vibrator effect:
In formula, PjRepresent the exciting force suffered by jth beam;ηjRepresent the Transverse Distribution of jth beam.
There is f=f againj, then:
According to specification, ζ=1%~5%, u is taken to rc beam bridge0≤L/600.For jth beam, to meet to scratch Degree requires that the value of exciting quality is:
Transverse Distribution η is not being measuredjBefore, exciting quality first can be estimated with theoretical value.
3. determine equivalent stiffness:
Embodiment 2:With reference to Fig. 1-Fig. 2, certain prefabricated PC concrete freely-supported Hollow Slab Beam Bridge across footpath 20m, top knot Structure is made up of 7 pieces of cored slabs, the wide b=1.25m of individual plates.According to design data, the cross section property parameter of beam is obtained:Bending resistance inertia Square I=1.391 × 106cm4;Torsional moment inertia IT=2.37 × 106cm4;Per linear meter(lin.m.) girder deadweight 11.2kN/m.Now intend surveying load When acting on the 4th beam, the Transverse Distribution of each beam.
First, designing quality vibrator.
1st, excited frequency is designed
To reach resonance effect, excited frequency Ying Yuliang free running frequency is identical.
2nd, exciting quality is designed
, can be in the hope of stiffness parameters according to design data:
According to linear interpolation, looking into articulated slab load relieving system influences the perpendicular mark table of line, obtains load action in the 4th beam When, the spaning middle section transverse distributing influence lines of each beam erect scale value, calculate Transverse Distribution is as follows:
Obviously, the Transverse Distribution η of the 4th beam4=0.161, take ζj=2%, A=0.05m are then:
mShakeTake 1000kg.
3rd, equivalent stiffness is calculated
kShake=4mShakeπ2f2=79604N/m
Then, Site Detection is carried out.
Step 1: install DH610V type electromagnetic type velocity sensors at the span centre position of every beam axis, the 4th beam Sensor can be moved slightly away from span centre (but being still located on axis), in order to the installation of vibrator.First, swashed using ambient vibration The method of encouraging tests to obtain the vertical intrinsic frequency f of single order of each hollow slab girder1、f2……fnWith damping ratios ζ1、ζ2……ζn, meter Calculation obtains average frequency value f.
Step 2: determine the vertical exciting quality of inertia mass vibrator.Because the quality of estimation is by assuming ζjAnd reason The f of opinion calculates what is got, not accurate enough.Now vibrator has designed completion, and rigidity is certain, can be original to reach resonance Increased and decreased in exciting quality.If the vibrator vibration frequency measured is larger, the exciting quality of vibrator can be reduced, conversely, then Increase certain exciting quality.The exciting quality of increase and decrease can be by vibration frequency inverse, until the frequency of quality vibrator is surveyed Untill value is equal to the average value f of each beam actual measurement intrinsic frequency.
Step 3: inertia mass vibrator is fixed on into the 4th beam bridge floor span centre position, bottom plate chemical anchor bolts with Beam body anchors together.Low frequency vibration pickup is arranged on each girder span centre position.Vibrator is in the 4th girder span with frequency f4, amplitude 0.05m carry out exciting, record exciting when each beam vertical motion speed time-domain signal.The amplitude of vibrator is by spiral shell Bolt and limiting plate are controlled, and both are very convenient in the regulation of short transverse.Excited frequency controls with metronome.
Step 4: determine the dynamic deflection maximum y of each girder span middle sectioni4:Rate signal is integrated to obtain in frequency domain The dynamic deflection curve of displacement signal, i.e. bridge, the average of the crest of maximum and the absolute value of trough is taken on dynamic deflection curve, made For the maximum dynamic deflection value y of No. i-th girder span middle section under the exciting effect in the 4th girder spani4
Step 5: calculate the spaning middle section Transverse Distribution of No. i-th beam under exciting effect effect in the 4th girder span ηi4

Claims (5)

  1. A kind of 1. method of quick test Hollow Slab Beam Bridge Transverse Distribution, it is characterised in that:This method comprises the following steps:
    Step 1: test to obtain the vertical intrinsic frequency f of single order of each hollow slab girder using ambient vibration advocate approach1、f2……fn With damping ratios ζ1、ζ2……ζn, wherein n is hollow sheet number, and average frequency value f is calculated;
    Step 2: according to the requirement of hollow slab girder maximum defluxion limit value, it is determined that the inertia mass vibrator installed in jth beam Vertical exciting quality:
    In formula:
    mShakeThe moving-mass of vibrator is represented,
    ζjThe damping ratios of jth beam are represented,
    MjThe gross mass of jth beam is represented,
    L represents the calculating across footpath of beam,
    A represents the displacement amplitude of vibrator,
    ηjRepresent the spaning middle section Transverse Distribution theoretical calculation of jth beam when unit force acts on the span centre of jth beam simultaneously Value;
    Step 3: inertia mass vibrator is installed above the span centre of jth beam, the fixed low frequency of position installation in each girder span Vibration pickup, vibrator is measured with frequency fj, amplitude A stable state exciting when each beam span centre vertical motion speed time-domain signal;
    Step 4: determine the dynamic deflection maximum y of each girder span middle sectionij:Rate signal is integrated in frequency domain to obtain displacement The dynamic deflection curve of signal, i.e. bridge, taken on dynamic deflection curve maximum crest and trough absolute value average, as Exciting acts on the maximum dynamic deflection value y of lower No. i-th girder span middle section in j girder spansij
    Step 5: calculate in j girder spans exciting effect under No. i-th girder span middle section Transverse Distribution ηij
    <mrow> <msub> <mi>&amp;eta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msqrt> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>f</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>2</mn> <msub> <mi>&amp;zeta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mfrac> <mi>f</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msqrt> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>f</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>2</mn> <msub> <mi>&amp;zeta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mfrac> <mi>f</mi> <msub> <mi>f</mi> <mi>i</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>.</mo> </mrow>
  2. 2. the inertia mass of a kind of method of quick test Hollow Slab Beam Bridge Transverse Distribution for described in claim 1 swashs Shake device, including, bottom plate, guide shaft and mass, guide shaft are cylinder, are fixedly connected at bottom plate center, are provided with bottom plate solid Determine hole and column, the upper surface of column is provided with caging bolt, it is characterised in that:Helical compression spring, spiral pressure are set with guide shaft Spring upper-end contact mass, mass are connected by linear bearing with guide shaft, and limited location is installed by screw thread on the top of guide shaft Plate.
  3. 3. inertia mass vibrator according to claim 2, it is characterised in that:Bottom plate is anchored at hollow by chemical bolt On plate-girder.
  4. 4. inertia mass vibrator according to claim 2, it is characterised in that:The vibration frequency of vibrator is by increasing and decreasing matter The quality of gauge block is adjusted.
  5. 5. inertia mass vibrator according to claim 2, it is characterised in that:The mass is to uppermost limit plate with The distance of square caging bolt is equal.
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