CN108509710A - A kind of parallel double width bridge analysis on stability against static wind load method - Google Patents
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Abstract
The present invention discloses a kind of parallel double width bridge analysis on stability against static wind load method, computational fluid dynamics calculate or wind tunnel test in two bridge main beam sections of upstream and downstream are included in model simultaneously, and convert four parameters (effective wind angle of attack of upstream girder, effective wind angle of attack of downstream girder ', the center spacing d and upper and lower height difference h) of two girders obtain the upstream girder under different parameters combine and downstream girder triadic Cantor set.Establish the space member system element finite model of upstream and downstream bridge simultaneously, for the torsion angle of upstream girder, the torsion angle of downstream girder ', four parameter iterations such as the center spacing d and upper and lower height difference h of two girders calculate the aerostatic instability of upstream and downstream bridge.The disturbing effect of upstream and downstream girder can be considered in the present invention, realizes the aerostatic instability fining analysis of parallel double width bridge, the more accurately quiet wind Instability Critical Wind Velocity of acquisition upstream and downstream bridge and the internal force under wind speed at different levels and displacement.
Description
Technical field
The invention belongs to Wind-resistance of Bridges design and research field, more particularly to a kind of parallel double width bridge analysis on stability against static wind load sides
Method.
Background technology
With the increasingly increase of the volume of traffic, bridge must have broader bridge floor and more tracks that could meet current need
It asks.It is real to avoid the wide structure stress (girder transverse bending moment is excessive, distortion and Shear Lag etc.) brought of bridge floor and aesthetic problem
Parallel double width bridge is often used in the engineering of border.Parallel double width bridge can be divided into two classes：The first kind is newly-built simultaneously parallel double
Width bridge, the second class extend a similar bridge to constitute parallel double width bridge near existing bridge.In recent years, parallel double width
Bridge is designed to apply more and more with the traffic capacity of its bigger, and the Fred Hartman bridges and Tacoma such as the U.S. are big
The flat victory bridge in bridge, the western bridge of Japanese tail road bridge and name port and China Fushan City, Guangdong Province and Shandong Province Qingdao bay Hong Dao
Channel Bridge etc..
With being constantly progressive for design theory and construction technology, bridge structure, which shows, to become across the development changed and softly changed greatly
Gesture, the rigidity of structure and damping constantly reduce, this so that long-span bridges are more prominent to the sensibility of wind.Work of the wind to bridge
With including Static behavior and power effect, charming appearance and behaviour Static behavior includes mean wind load effect and charming appearance and behaviour static(al) unstability again, with power
Unstability is compared, static(al) unstability no any tendency before occurring, sudden strong, destructive bigger.Therefore, charming appearance and behaviour Static behavior has
Important researching value.
Quiet wind unstability refers to structure under the effect of given wind speed, and girder bends and torsional deflection, on the one hand changes
The rigidity of structure on the other hand because the variation of Structure Attitude changes the size of wind load, and increases the deformation of structure, most in turn
The phenomenon that leading to structural instability eventually.With the growth of wind speed, when the drag increment caused by malformation is less than external load increment,
Quiet wind unstability will occur.Quiet wind unstability is a kind of embodiment of mean wind load and malformation coupling.Quiet wind unstability jeopardizes
Its generation should be absolutely avoided in bridge security.
Similar with traditional single width bridge, the parallel double width bridge of large span equally exists the possibility of quiet wind unstability, need to be into
Row analysis on stability against static wind load.But the difference is that, clear spacing is generally little between twin decks, gas with traditional single width bridge
Stream can generate complicated aerodynamic interference effect between upstream and downstream bridge floor when flowing through, may be to the static(al) and power wind resistance of bridge
Certain influence can be generated.
Invention content
Goal of the invention：For in the prior art not specifically for parallel double width bridge progress analysis on stability against static wind load to make
The problem of Cheng Jingfeng unstabilitys jeopardize bridge security provides a kind of parallel double width bridge analysis on stability against static wind load method.
Technical solution：Girder triadic Cantor set is the basic parameter for calculating aerostatic instability, generally uses force test in wind tunnel
Or Fluid Mechanics Computation technology identification.There are aerodynamic interference effects between two girders of parallel double width bridge, so parallel double width
The triadic Cantor set of bridge girder is different from single girder triadic Cantor set.The triadic Cantor set of upstream girder and downstream girder are not yet
Together, and both it is influenced by four parameters：Effective wind angle of attack of upstream girder, effective wind angle of attack of downstream girder ',
The center spacing d and upper and lower height difference h of two girders, as shown in Figure 1.Therefore, either upstream girder triadic Cantor set, or under
Girder triadic Cantor set is swum, is all the function of aforementioned four parameter respectively.Under different wind speed, vertical position can occur for bridge
Shifting, lateral displacement and torsional displacement cause the spatial attitude of bridge different, therefore aforementioned four parameter becomes as wind speed increases
Change.On the other hand, under certain grade of wind speed, aforementioned four parameter is also different at different location along bridge length direction.With wind
It, need to be same by upstream main beam section and downstream main beam section when hole dynamometer check or Fluid Mechanics Computation technology identification triadic Cantor set
When be included in model, and convert aforementioned four parameter, measure the triadic Cantor set under various combination.The transformation range of each parameter is most
Amount is big, and the combination of four parameters is more as possible, can just be covered in the case where analysis on stability against static wind load is likely to occur in the process in this way.
In order to solve the above technical problems, the present invention provides a kind of parallel double width bridge analysis on stability against static wind load method, including it is as follows
Step：
1) Numerical Wind Tunnel or physics wind tunnel model, are built, the model is then based on and obtains upstream girder and downstream girder
The correspondence of triadic Cantor set and aforementioned four parameter；The triadic Cantor set includes resistance coefficient, lift coefficient and lift
Moment coefficient, four parameters include effective wind angle of attack of upstream girder, effective wind angle of attack of downstream girder ', two girders
Centre of twist spacing d and upper and lower height difference h；
2) spatial finite element model, is established, while including the information of upstream bridge and downstream bridge, upstream bridge and downstream
The relative position relation of bridge is consistent with real bridge, then carries out geometrical non-linearity under Gravitative Loads and solves；
3) initial wind speed V, is set0With wind speed step delta V, current wind speed Vi=V0, and set iterations upper limit Nmax；
4) torsion angle of upstream girder each unit, is extracted from spatial finite element modeli, downstream girder each unit torsion
Rotational angle thetai', the center spacing d of upstream girder each unit and downstream girder corresponding unitiWith upper and lower height difference hi；
5), according to the torsion angle of the upstream girder each unit obtained in step 4)i, downstream girder each unit torsion angle
θi' and initial wind angle of attack0, calculate effective wind angle of attack of upstream girder each uniti(=α0+θi) and downstream girder each unit
Effective wind angle of attacki' (=α0+θ′i)；Then according to four parameter combination (αi,α′i,di,hi) utilize quintuple space interpolation method point
Not Ji Suan upstream girder and downstream girder each unit triadic Cantor set；
6), in current wind speed ViUnder, calculate the across-wind dynamic load P for acting on upstream girder each unitHi, vertical wind excitation PVi
With torsional moment PMiAnd the across-wind dynamic load P ' of downstream girder each unitHi, vertical wind excitation P 'ViWith torsional moment P 'Mi；
7), upstream girder, downstream girder each unit on apply across-wind dynamic load P respectivelyHiWith P 'Hi, vertical wind excitation
PViWith P 'Vi, torsional moment PMiWith P 'Mi, bridge structure geometrical non-linearity solution is carried out, the torsion of upstream girder each unit is obtained
Angle θi, downstream girder each unit torsion angle 'i, upstream girder each unit and downstream girder corresponding unit centre of twist spacing
diWith upper and lower height difference hi, judge whether the Euclid norm of this four parameters is respectively smaller than equal to permissible value ε according to the following formula1、
ε2、ε3And ε4：
In formula, N is the unit sum of girder；K is present load step number；I is beam element serial number；
8) if any formula, in above-mentioned four formula is invalid, repeatedly step 5) -7)；If iterations reach iteration
Number upper limit Nmax, then current wind speed be difficult to restrain, this season current wind speed Vi+1=ViThen Δ V shortens wind speed step-length, returns
Step 5) is returned, step 5) -7 is repeated)；If wind speed step-length is less than predetermined value, calculating terminates；If above-mentioned four formula all at
Vertical, then current wind speed numerical convergence, exports result of calculation, wherein and result of calculation includes bridge structure deformation parameter, this
Seasonal current wind speed Vi+1=Vi+ Δ V repeats step 5) -7)；
9), the result of calculation obtained according to step 8) obtains the quiet wind Instability Critical Wind Velocity of upstream bridge and downstream bridge
With unstability form.
Further, the triadic Cantor set and its four parameters of upstream girder and downstream girder are obtained in the step 1)
Correspondence is as follows：Upstream main beam section and downstream main beam section are included in Numerical Wind Tunnel or physics wind-tunnel simultaneously
Model, and aforementioned four parameter is converted, measure the triadic Cantor set under various combination.By the different combination of four parameters and its right
The upstream and downstream main beam section triadic Cantor set answered is stored in a manner of array can call and obtains upstream girder and downstream girder
Triadic Cantor set and its four parameters correspondence.
Further, the step 6) is fallen into a trap the across-wind dynamic load P that can be regarded as used in upstream girder each unitHi, vertical wind lotus
Carry PViWith torsional moment PMiAnd the across-wind dynamic load P ' of downstream girder each unitHi, vertical wind excitation P 'ViWith torsional moment P 'Mi
It is as follows：
Upstream girder
Downstream girder
In formula, CHi、CViAnd CMiResistance coefficient, lift coefficient and the lift moment coefficient of upstream girder are indicated respectively；C′Hi、
C′ViWith C 'MiResistance coefficient, lift coefficient and the lift moment coefficient of downstream girder are indicated respectively；B indicates the width of girder；liWith
l′iThe length of upstream girder and downstream girder each unit is indicated respectively；ρ is atmospheric density；ViFor current wind speed.
Further, it is all made of arc-length methods progress bridge structure geometrical non-linearity solution in the step 2) and step 7).
Further, the predetermined value of step 8) the apoplexy trot length is 0~0.5m/s.
Further, determine that quiet wind Instability Critical Wind Velocity is as follows in the step 9)：First according to bridge
The relationship of malformation and wind speed draws bridge structure deformation-wind speed curve, then according to the section of maximum slope in curve,
Obtain quiet wind Instability Critical Wind Velocity.
Compared with the prior art, the advantages of the present invention are as follows：
In existing pertinent literature and patent, influence of the parameter (the wind angle of attack) to triadic Cantor set is only considered,
The mean wind load of girder cannot accurately be calculated.For parallel double width bridge, under certain grade of wind speed, the effective wind angle of attack of upstream girder, under
It is longitudinally variation that 4 parameters such as effective wind angle of attack of girder, the spacing of upstream and downstream girder and height difference, which are swum, along bridge.Due to flat
The aerodynamic interference effect of row double width bridge, this 4 parameters can influence triadic Cantor set.Therefore, in order to accurately calculate the quiet of girder
Wind load calculates aerostatic instability in turn, it is necessary to while considering this influence of 4 parameters to triadic Cantor set.On the other hand, exist
It in existing pertinent literature and patent, calculates and there was only single bridge in the finite element model of aerostatic instability, even for parallel double
Width bridge, the deformation under mean wind load effect is also to be calculated separately for every width bridge, can not obtain under wind speed at different levels upstream with
The relative position relation of downstream bridge.The parallel double width bridge analysis on stability against static wind load method of the present invention, it is contemplated that upstream girder is effective
Shadow of 4 parameters such as the wind angle of attack, effective wind angle of attack of downstream girder, the spacing of upstream and downstream girder and height difference to triadic Cantor set
It rings, and also includes upstream and downstream bridge simultaneously in finite element model, the synchronous quiet wind deformation for calculating two width bridges and phase
To position relationship, the aerostatic instability fining analysis of parallel double width bridge may be implemented, obtain and consider the upper of aerodynamic interference effect
Swim the quiet wind Instability Critical Wind Velocity and unstability form of bridge.
Description of the drawings
Fig. 1 is the upstream and downstream main beam section schematic diagram of parallel double width bridge；
Fig. 2 is the mean wind load and relevant parameter schematic diagram acted in Bridge Sections.
Specific implementation mode
With reference to the accompanying drawings and detailed description, the present invention is furture elucidated.Embodiments described herein are only
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, ordinary skill people
Member's obtained other embodiment without making creative work belongs to the range that the present invention is protected.
The present invention includes the upstream bridge being mutually parallel and downstream bridge, is included the following steps：
1) it, is based on Fluid Mechanics Computation technology (Numerical Wind Tunnel) or wind tunnel test (physics wind-tunnel) identifies upstream and downstream
Bridge main beam section triadic Cantor set, the triadic Cantor set include resistance coefficient, lift coefficient and lift moment coefficient, such as Fig. 2
It is shown.When identifying triadic Cantor set, upstream main beam section and downstream main beam section are included in Numerical Wind Tunnel or physics wind-tunnel simultaneously
Model, and convert four parameters：Effective wind angle of attack of upstream girder, effective wind angle of attack of downstream girder ', the torsions of two girders
Turn center spacing d and upper and lower height difference h.The triadic Cantor set for obtaining upstream girder and downstream girder is corresponding with aforementioned four parameter
Relationship, and by four parameter various combinations and its corresponding upstream and downstream main beam section triadic Cantor set by can call in a manner of array into
Row storage, the calculating for aerodynamic force suffered by main beam section lay the foundation.
2), establish spatial finite element model, while including upstream bridge and downstream bridge, the relative position relation of the two with
Real bridge is consistent, then carries out geometrical non-linearity under Gravitative Loads and solves.
3) initial wind speed V, is set0With wind speed step delta V, current wind speed Vi=V0, and set iterations upper limit Nmax。
4) torsion angle of upstream girder each unit, is extractedi, downstream girder each unit torsion angle 'i, each list of upstream girder
The center spacing d of member and downstream girder corresponding unitiWith upper and lower height difference hi。
5), according to torsion angle and initial wind angle of attack0Calculate effective wind angle of attack of upstream girder each uniti(=α0+θi) and
Effective wind angle of attack of downstream girder each unit 'i(=α0+θ′i).Then according to four parameter combination (αi,α′i,di,hi) utilize five
Dimension space interpolation method calculates separately the triadic Cantor set of upstream girder and downstream girder each unit.
6), in current wind speed ViUnder, calculate the across-wind dynamic load P for acting on upstream girder each unitHi, vertical wind excitation PVi
With torsional moment PMiAnd the across-wind dynamic load P ' of downstream girder each unitHi, vertical wind excitation P 'ViWith torsional moment P 'Mi：
Upstream girder
Downstream girder
In formula, CHi、CViAnd CMiResistance coefficient, lift coefficient and the lift moment coefficient of upstream girder are indicated respectively；C′Hi、
C′ViWith C 'MiResistance coefficient, lift coefficient and the lift moment coefficient of downstream girder are indicated respectively；B indicates the width of girder；liWith
l′iThe length of upstream girder and downstream girder each unit is indicated respectively；ρ is atmospheric density；ViFor current wind speed.
7), upstream girder, downstream girder each unit on apply across-wind dynamic load P respectivelyHiWith P 'Hi, vertical wind excitation
PViWith P 'Vi, torsional moment PMiWith P 'Mi, bridge structure geometrical non-linearity solution is carried out, the torsion of upstream girder each unit is obtained
Angle θi, downstream girder each unit torsion angle 'i, upstream girder each unit and downstream girder corresponding unit centre of twist spacing
diWith upper and lower height difference hi, judge whether the Euclid norm of this four parameters is respectively smaller than equal to permissible value ε according to the following formula1、
ε2、ε3And ε4：
In formula, N is the unit sum of girder；K is present load step number；I is beam element serial number.
8) if any formula, in above-mentioned four formula is invalid, repeatedly step 5) -7)；If iterations reach iteration
Number upper limit Nmax, then current wind speed be difficult to restrain, this season current wind speed Vi+1=ViThen Δ V shortens wind speed step-length, returns
Step 5) is returned, step 5) -7 is repeated)；If wind speed step-length is less than predetermined value, calculating terminates；If above-mentioned four formula all at
Vertical, then current wind speed numerical convergence, exports result of calculation, wherein and result of calculation includes bridge structure deformation parameter, this
Seasonal current wind speed Vi+1=Vi+ Δ V repeats step 5) -7).
9), the result of calculation obtained according to step 8) obtains the quiet wind Instability Critical Wind Velocity of upstream bridge and downstream bridge
With unstability form；
Further, arc-length methods are used to carry out bridge structure geometrical non-linearity solution in step 2) and step 7).
Further, permissible value ε in step 7)1、ε2、ε3And ε4It can be identical value, value can also be different,
The sensibility that triadic Cantor set influences can be determined according to parameter, smaller permissible value is used to the stronger parameter of sensibility,
The parameter weaker to sensibility uses larger permissible value.
Further, step 8) apoplexy trot length predetermined value, as an optimization, can between 0~0.5m/s value.
Further, determine that quiet wind Instability Critical Wind Velocity includes the following steps in step 9)：First according to bridge structure
The relationship of deformation and wind speed is drawn bridge structure deformation-wind speed curve and is obtained then according to the section of maximum slope in curve
Quiet wind Instability Critical Wind Velocity.
Claims (6)
1. a kind of parallel double width bridge analysis on stability against static wind load method, which is characterized in that include the following steps：
1) Numerical Wind Tunnel or physics wind tunnel model, are built, is then based on three points that the model obtains upstream girder and downstream girder
The correspondence of force coefficient and four parameters；The triadic Cantor set includes resistance coefficient, lift coefficient and lift moment coefficient, institute
State four parameters include effective wind angle of attack of upstream girder, effective wind angle of attack of downstream girder ', the centres of twist of two girders
Spacing d and upper and lower height difference h；
2) spatial finite element model, is established, while including the information of upstream bridge and downstream bridge, upstream bridge and downstream bridge
Relative position relation it is consistent with real bridge, then carry out geometrical non-linearity under Gravitative Loads and solve；
3) initial wind speed V, is set0With wind speed step delta V, current wind speed Vi=V0, and set iterations upper limit Nmax；
4) torsion angle of upstream girder each unit, is extracted from spatial finite element modeli, downstream girder each unit torsion angle
θi', the center spacing d of upstream girder each unit and downstream girder corresponding unitiWith upper and lower height difference hi；
5), according to the torsion angle of the upstream girder each unit obtained in step 4)i, downstream girder each unit torsion anglei' with
And initial wind angle of attack0, calculate effective wind angle of attack of upstream girder each uniti(=α0+θi) and downstream girder each unit have
Imitate wind angle of attacki' (=α0+θi')；Then according to four parameter combination (αi,αi',di,hi) counted respectively using quintuple space interpolation method
Count the triadic Cantor set of trip girder and downstream girder each unit in；
6), in current wind speed ViUnder, calculate the across-wind dynamic load P for acting on upstream girder each unitHi, vertical wind excitation PViAnd torsion
Torque PMiAnd the across-wind dynamic load P of downstream girder each unitH'i, vertical wind excitation PV'iWith torsional moment PM'i；
7), upstream girder, downstream girder each unit on apply across-wind dynamic load P respectivelyHiAnd PH'i, vertical wind excitation PViWith
PV'i, torsional moment PMiAnd PM'i, bridge structure geometrical non-linearity solution is carried out, the torsion angle of upstream girder each unit is obtainedi、
The torsion angle of downstream girder each uniti', the centre of twist spacing d of upstream girder each unit and downstream girder corresponding unitiWith it is upper
Lower height difference hi, judge whether the Euclid norm of this four parameters is respectively smaller than equal to permissible value ε according to the following formula1、ε2、ε3With
ε4：
In formula, N is the unit sum of girder；K is present load step number；I is beam element serial number；
8) if any formula, in above-mentioned four formula is invalid, repeatedly step 5) -7)；If iterations reach iterations
Upper limit Nmax, then current wind speed be difficult to restrain, this season current wind speed Vi+1=ViThen Δ V shortens wind speed step-length, return to step
It is rapid 5), repeat step 5) -7)；If wind speed step-length is less than predetermined value, calculating terminates；If above-mentioned four formula is all set up,
Current wind speed numerical convergence, exports result of calculation, wherein result of calculation includes bridge structure deformation parameter, this season
Current wind speed Vi+1=Vi+ Δ V repeats step 5) -7)；
9), the result of calculation obtained according to step 8) obtains quiet wind Instability Critical Wind Velocity and the mistake of upstream bridge and downstream bridge
Steady form.
2. a kind of parallel double width bridge analysis on stability against static wind load method according to claim 1, which is characterized in that the step 1)
The triadic Cantor set and the correspondence of its four parameters of middle acquisition upstream girder and downstream girder are as follows：It will be upper
Trip main beam section and downstream main beam section are included in Numerical Wind Tunnel or physics wind tunnel model simultaneously, and convert aforementioned four parameter, survey
Obtain the triadic Cantor set under various combination；By the different combination of four parameters and its corresponding three component of upstream and downstream main beam section
Coefficient is stored and is obtained the triadic Cantor set and its four parameters of upstream girder and downstream girder in a manner of array can call
Correspondence.
3. a kind of parallel double width bridge analysis on stability against static wind load method according to claim 1, which is characterized in that the step 6)
Fall into a trap the across-wind dynamic load P that can be regarded as used in upstream girder each unitHi, vertical wind excitation PViWith torsional moment PMiAnd downstream girder
The across-wind dynamic load P of each unitH'i, vertical wind excitation PV'iWith torsional moment PM'iIt is as follows：
In formula, CHi、CViAnd CMiResistance coefficient, lift coefficient and the lift moment coefficient of upstream girder are indicated respectively；C'Hi、C'ViWith
C'MiResistance coefficient, lift coefficient and the lift moment coefficient of downstream girder are indicated respectively；B indicates the width of girder；liAnd li' point
Not Biao Shi upstream girder and downstream girder each unit length；ρ is atmospheric density；ViFor current wind speed.
4. a kind of parallel double width bridge analysis on stability against static wind load method according to claim 1, which is characterized in that the step 2)
Bridge structure geometrical non-linearity solution is carried out with arc-length methods are all made of in step 7).
5. a kind of parallel double width bridge analysis on stability against static wind load method according to claim 1, which is characterized in that the step 8)
The predetermined value of apoplexy trot length is 0~0.5m/s.
6. a kind of parallel double width bridge analysis on stability against static wind load method according to claim 1, which is characterized in that the step 9)
The middle quiet wind Instability Critical Wind Velocity of determination is as follows：First according to the relationship of bridge structure deformation and wind speed, bridge is drawn
Girder construction deformation-wind speed curve obtains quiet wind Instability Critical Wind Velocity then according to the section of maximum slope in curve.
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| CN110991028B (en) * | 2019-06-04 | 2023-10-10 | 中国公路工程咨询集团有限公司 | Driving stability analysis method and device for bridge deck |
| CN110580380A (en) * | 2019-08-15 | 2019-12-17 | 广州大学 | Method and device for processing equivalent static wind load data of building and storage medium |
| CN110619150A (en) * | 2019-08-15 | 2019-12-27 | 广州大学 | Load analysis method and device considering modal coupling effect and storage medium |
| CN110619150B (en) * | 2019-08-15 | 2023-03-28 | 广州大学 | Load analysis method and device considering modal coupling effect and storage medium |
| CN110580380B (en) * | 2019-08-15 | 2023-04-25 | 广州大学 | Method, device and storage medium for processing building equivalent static wind load data |
| CN110807222A (en) * | 2019-11-06 | 2020-02-18 | 苏交科集团股份有限公司 | Method for quickly identifying static aerodynamic coefficient of section of main beam |
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