CN108509710A - A kind of parallel double width bridge analysis on stability against static wind load method - Google Patents

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

A wind-static stability analysis method for parallel double-width bridges

technical field

The invention belongs to the field of wind-resistant design and research of bridges, in particular to a wind-static stability analysis method for parallel double-width bridges.

Background technique

With the increasing traffic volume, bridges must have wider decks and more lanes to meet the traffic demand. In order to avoid the structural stress (excessive transverse bending moment of the main girder, distortion and shear lag, etc.) and aesthetic problems caused by the bridge deck being too wide, parallel double-width bridges are often used in actual projects. Parallel double-width bridges can be divided into two categories: the first type is a parallel double-width bridge newly built at the same time, and the second type is to expand a similar bridge near an existing bridge to form a parallel double-width bridge. In recent years, parallel double-width bridges have been increasingly designed and applied due to their greater traffic capacity, such as the Fred Hartman Bridge and Tacoma Bridge in the United States, the Onomichi Bridge and Minggangxi Bridge in Japan, and the Pingsheng Bridge and Pingsheng Bridge in Foshan City, Guangdong Province, my country. Red Island Waterway Bridge, Qingdao Bay, Shandong Province, etc.

With the continuous improvement of design theory and construction technology, the bridge structure presents a development trend of long-span and softness, and the structural stiffness and damping continue to decrease, which makes the long-span bridge structure more sensitive to wind. The effects of wind on bridges include static and dynamic effects, and wind-induced static effects include static wind loads and wind-induced static instability. Compared with dynamic instability, static instability occurs without any warning, sudden Stronger, more destructive. Therefore, the aeostatic effect has important research value.

Static wind instability refers to the bending and torsional deformation of the main girder under the action of a given wind speed. On the one hand, the structural stiffness is changed, and on the other hand, the wind load is changed due to the change of the structural posture, which in turn increases the structure. deformation, which eventually leads to structural instability. With the increase of wind speed, when the resistance increment caused by structural deformation is smaller than the external load increment, aerostatic instability will occur. Aeolian instability is a manifestation of the coupling effect of aerostatic loads and structural deformations. The static wind instability endangers the safety of the bridge and should be absolutely avoided.

Similar to traditional single-width bridges, long-span parallel double-width bridges also have the possibility of aerostatic instability, and aerostatic stability analysis is required. However, the difference from the traditional single-width bridge is that the net distance between the double-width bridge decks is generally not large, and when the airflow passes by, complex aerodynamic interference effects will be generated between the upstream and downstream bridge decks, which may affect the static and dynamic forces of the bridge. The dynamic wind resistance performance has a certain influence.

Contents of the invention

Purpose of the invention: To provide an aerostatic stability analysis method for parallel double-width bridges in view of the problem that there is no aerostatic stability analysis for parallel double-width bridges in the prior art, resulting in aerostatic instability that endangers bridge safety.

Technical solution: The three-component force coefficient of the main girder is the basic parameter for calculating static wind stability, which is generally identified by wind tunnel force test or computational fluid dynamics technology. There is an aerodynamic interference effect between the two girders of a parallel double-width bridge, so the three-component force coefficient of the main girder of a parallel double-width bridge is different from that of a single main girder. The three-component force coefficient of the upstream girder is also different from that of the downstream girder, and both are affected by four parameters: the effective wind attack angle α of the upstream girder, the effective wind attack angle α' of the downstream girder, the two main girders The center distance d and the height difference h between the beams are shown in Figure 1. Therefore, both the three-component force coefficient of the upstream main beam and the three-component force coefficient of the downstream main beam are functions of the above four parameters. Under different wind speeds, the bridge will undergo vertical displacement, lateral displacement, and torsional displacement, resulting in different spatial postures of the bridge. Therefore, the above four parameters change with the increase of wind speed. On the other hand, at a certain level of wind speed, the above four parameters are also different at different positions along the length of the bridge. When using wind tunnel force test or computational fluid dynamics technology to identify the three-component force coefficient, it is necessary to include the upstream main beam section and the downstream main beam section into the model at the same time, and change the above four parameters to measure the three-component force under different combinations coefficient. The transformation range of each parameter is as large as possible, and the combination of the four parameters is as many as possible, so as to cover possible situations that may occur during the static wind stability analysis.

In order to solve the above-mentioned technical problems, the present invention provides a method for analyzing the static wind stability of a parallel double-width bridge, which includes the following steps:

1), construct numerical wind tunnel or physical wind tunnel model, obtain the three-component force coefficient of upstream girder and downstream main girder and the corresponding relationship of above-mentioned four parameters based on this model then; Described three-component force coefficient comprises drag coefficient, lift force coefficient and lift moment coefficient, the four parameters include the effective wind attack angle α of the upstream main girder, the effective wind attack angle α' of the downstream main girder, the torsion center distance d of the two main girders, and the height difference h;

2) Establish a spatial finite element model, including the information of the upstream bridge and the downstream bridge. The relative position relationship between the upstream bridge and the downstream bridge is consistent with the real bridge, and then solve the geometric nonlinearity under the action of self-weight;

3), set the initial wind speed V ₀ and the wind speed step size ΔV, the current wind speed V _i =V ₀ , and set the upper limit N _max of the number of iterations;

4) From the spatial finite element model, extract the torsion angle θ _i of each unit of the upstream main beam, the torsion angle θ _i ' of each unit of the downstream main beam, the center-to-center distance d _i and Height difference h _i ;

5) According to the torsion angle θ _i of each unit of the upstream main beam obtained in step 4), the torsion angle θ _i ' of each unit of the downstream main beam and the initial wind attack angle α ₀ , calculate the effective wind of each unit of the upstream main beam The attack angle α _i (=α ₀ +θ _i ) and the effective wind attack angle α _i '(=α ₀ +θ′ _i ) of each unit of the downstream girder; then according to the combination of four parameters (α _i ,α′ _i ,d _i , h _i ) Use the five-dimensional space interpolation method to calculate the three-component force coefficients of each unit of the upstream main beam and the downstream main beam;

6) Under the current wind speed V _i , calculate the lateral wind load P _Hi , vertical wind load P _Vi and torsional moment P _Mi acting on each unit of the upstream main girder, and the lateral wind load P′ _Hi of each unit of the downstream main girder , vertical wind load P′ _Vi and torsional moment P′ _Mi ;

7) Apply transverse wind loads P _Hi and P′ _Hi , vertical wind loads P _Vi and P′ _Vi , torsional moments P _Mi and P′ _Mi to the units of the upstream main girder and downstream main girder respectively, and carry out the bridge structure Geometrically nonlinear solution to obtain the torsion angle θ _i of each unit of the upstream main beam, the torsion angle θ′ _i of each unit of the downstream main beam, the torsion center distance d _i and the height difference between each unit of the upstream main beam and the corresponding unit of the downstream main beam h _i , judge whether the Euclidean norms of these four parameters are less than or equal to the allowable values ε ₁ , ε ₂ , ε ₃ and ε ₄ according to the following formula:

In the formula, N is the total number of units of the main beam; k is the number of the current load step; i is the serial number of the beam unit;

8) If any of the above four formulas is not established, repeat steps 5)-7); if the number of iterations reaches the upper limit N _max of the number of iterations, it is difficult for the current wind speed to converge. At this time, the current wind speed V _i+1 =V _i - ΔV, then shorten the wind speed step, return to step 5), repeat steps 5)-7); if the wind speed step is less than the predetermined value, the calculation ends; if all the above four formulas are established, the current wind speed calculation result converges, and the calculation result is output , wherein the calculation result includes the deformation parameters of the bridge structure, at this time the current wind speed V _i+1 =V _i +ΔV, repeat steps 5)-7);

9), according to the calculation result obtained in step 8), obtain the critical wind speed and instability shape of the upstream bridge and the downstream bridge for static wind instability.

Further, the specific steps for obtaining the corresponding relationship between the three-component force coefficients of the upstream girder and the downstream girder and their four parameters in the step 1) are as follows: simultaneously incorporate the upstream girder section and the downstream girder section into the numerical wind tunnel or Physical wind tunnel model, and transform the above four parameters, and measure the three-component force coefficient under different combinations. The different combinations of the four parameters and the corresponding three-component force coefficients of the upstream and downstream main girder sections are stored in a callable array, and the corresponding relationship between the three-component force coefficients of the upstream main girder and the downstream main girder and their four parameters is obtained.

Further, the step 6) calculates the lateral wind load P _Hi , vertical wind load P _Vi and torsional moment P _Mi acting on each unit of the upstream main beam, and the lateral wind load P′ _Hi , The specific steps of vertical wind load P′ _Vi and torsional moment P′ _Mi are as follows:

Upstream girder

downstream girder

In the formula, C _Hi , C _Vi and C _Mi represent the drag coefficient, lift coefficient and lift moment coefficient of the upstream girder respectively; C′ _Hi , C′ _Vi and C′ _Mi represent the drag coefficient, lift coefficient and lift moment coefficient of the downstream girder respectively lift moment coefficient; B represents the width of the main girder; l _i and l′ _i represent the lengths of each unit of the upstream main girder and downstream main girder respectively; ρ is the air density; V _i is the current wind speed.

Further, in the step 2) and step 7), the arc length method is used to solve the geometric nonlinearity of the bridge structure.

Further, the predetermined value of the wind speed step in step 8) is 0-0.5m/s.

Further, the specific steps for determining the critical wind speed of static wind instability in the step 9) are as follows: first, draw the bridge structure deformation-wind speed curve according to the relationship between the bridge structure deformation and the wind speed, and then according to the section with the largest slope in the curve, obtain Critical wind speed for static wind instability.

Compared with the prior art, the present invention has the advantages of:

In the existing relevant literature and patents, only the influence of one parameter (wind attack angle) on the three-component force coefficient is considered, and the static wind load of the main girder cannot be accurately calculated. For parallel double-width bridges, at a certain level of wind speed, four parameters, including the effective wind attack angle of the upstream main girder, the effective wind attack angle of the downstream main girder, the spacing and height difference between the upstream and downstream main girders, change along the longitudinal direction of the bridge. Due to the aerodynamic interference effect of the parallel double-width bridge, these four parameters will all affect the three-component force coefficient. Therefore, in order to accurately calculate the static wind load of the main girder and then calculate the static wind stability, it is necessary to consider the influence of these four parameters on the three-component force coefficient at the same time. On the other hand, in the existing relevant literature and patents, there is only a single bridge in the finite element model for calculating static aerodynamic stability. Even for parallel double-width bridges, the deformation under static wind loads is calculated separately for each bridge, which cannot Obtain the relative positional relationship of the upstream and downstream bridges at various wind speeds. The static wind stability analysis method of the parallel double-width bridge of the present invention considers the effective wind attack angle of the upstream main girder, the effective wind attack angle of the downstream main girder, the spacing and height difference between the upstream and downstream main girders, etc. to the three-component force coefficient. In addition, the upstream and downstream bridges are also included in the finite element model, and the static wind deformation and relative position relationship of the two bridges are calculated synchronously, which can realize the refined analysis of the static wind stability of the parallel double bridges, and obtain the upstream bridge considering the aerodynamic interference effect. The critical wind speed and instability shape of the bridge's static wind instability.

Description of drawings

Figure 1 is a schematic diagram of the cross-section of the upstream and downstream main girders of a parallel double-width bridge;

Figure 2 is a schematic diagram of the static wind load and related parameters acting on the bridge section.

Detailed ways

The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. The embodiments described in the present invention are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, other embodiments obtained by persons of ordinary skill in the art without making creative efforts all fall within the protection scope of the present invention.

The present invention comprises mutually parallel upstream bridge and downstream bridge, comprises the following steps:

1), based on computational fluid dynamics technology (numerical wind tunnel) or wind tunnel test (physical wind tunnel), the three-component force coefficients of the upstream and downstream bridge girder sections are identified, and the three-component force coefficients include drag coefficient, lift coefficient and lift coefficient. Moment coefficient, as shown in Figure 2. When identifying the three-component force coefficient, the upstream main beam section and the downstream main beam section are included in the numerical wind tunnel or physical wind tunnel model, and four parameters are transformed: the effective wind attack angle α of the upstream main beam, the effective wind angle α of the downstream main beam The angle of attack α', the torsion center distance d and the height difference h between the two main girders. Obtain the corresponding relationship between the three-component force coefficients of the upstream main beam and the downstream main beam and the above four parameters, and store the different combinations of the four parameters and the corresponding three-component force coefficients of the upstream and downstream main beam sections in a callable array. It lays the foundation for the calculation of the aerodynamic force on the main beam section.

2) Establish a spatial finite element model, including both the upstream bridge and the downstream bridge. The relative position relationship between the two is consistent with the real bridge, and then solve the geometric nonlinearity under the action of self-weight.

3) Set the initial wind speed V ₀ and the wind speed step size ΔV, the current wind speed V _i =V ₀ , and set the upper limit N _max of the number of iterations.

4) Extract the torsion angle θ _i of each unit of the upstream main beam, the torsion angle θ′ _i of each unit of the downstream main beam, the center distance d _i and the height difference h _i between each unit of the upstream main beam and the corresponding unit of the downstream main beam.

5) Calculate the effective wind attack _{angle α i (} =α ₀ +θ _i ) of each unit of the upstream main beam and the effective wind attack angle α′ _i (= α ₀ +θ′ _i ). Then according to the combination of four parameters (α _i , α′ _i , d _i , h _i ), the three-component force coefficients of each unit of the upstream main beam and the downstream main beam are respectively calculated by using the five-dimensional space interpolation method.

6) Under the current wind speed V _i , calculate the lateral wind load P _Hi , vertical wind load P _Vi and torsional moment P _Mi acting on each unit of the upstream main girder, and the lateral wind load P′ _Hi of each unit of the downstream main girder , vertical wind load P′ _Vi and torsional moment P′ _Mi :

Upstream girder

downstream girder

In the formula, C _Hi , C _Vi and C _Mi represent the drag coefficient, lift coefficient and lift moment coefficient of the upstream girder respectively; C′ _Hi , C′ _Vi and C′ _Mi represent the drag coefficient, lift coefficient and lift moment coefficient of the downstream girder respectively lift moment coefficient; B represents the width of the main girder; l _i and l′ _i represent the lengths of each unit of the upstream main girder and downstream main girder respectively; ρ is the air density; V _i is the current wind speed.

7) Apply transverse wind loads P _Hi and P′ _Hi , vertical wind loads P _Vi and P′ _Vi , torsional moments P _Mi and P′ _Mi to the units of the upstream main girder and downstream main girder respectively, and carry out the bridge structure Geometrically nonlinear solution to obtain the torsion angle θ _i of each unit of the upstream main beam, the torsion angle θ′ _i of each unit of the downstream main beam, the torsion center distance d _i and the height difference between each unit of the upstream main beam and the corresponding unit of the downstream main beam h _i , judge whether the Euclidean norms of these four parameters are less than or equal to the allowable values ε ₁ , ε ₂ , ε ₃ and ε ₄ according to the following formula:

In the formula, N is the total number of units of the main beam; k is the number of the current load step; i is the serial number of the beam unit.

8) If any of the above four formulas is not established, repeat steps 5)-7); if the number of iterations reaches the upper limit N _max of the number of iterations, it is difficult for the current wind speed to converge. At this time, the current wind speed V _i+1 =V _i - ΔV, then shorten the wind speed step, return to step 5), repeat steps 5)-7); if the wind speed step is less than the predetermined value, the calculation ends; if all the above four formulas are established, the current wind speed calculation result converges, and the calculation result is output , wherein the calculation result includes the deformation parameters of the bridge structure, at this time the current wind speed V _i+1 =V _i +ΔV, repeat steps 5)-7).

9), according to the calculation result obtained in step 8), obtain the static wind instability critical wind speed and the instability form of the upstream bridge and the downstream bridge;

Further, in step 2) and step 7), the arc length method is used to solve the geometric nonlinearity of the bridge structure.

Furthermore, the allowable values ε ₁ , ε ₂ , ε ₃ and ε ₄ in step 7) can be the same value or different values, which can be determined according to the sensitivity of the parameters to the influence of the three-component force coefficient. A smaller allowable value is used for a more sensitive parameter, and a larger allowable value is used for a less sensitive parameter.

Furthermore, the predetermined value of the wind speed step in step 8) can be selected as an optimization value between 0 and 0.5m/s.

Furthermore, the determination of the critical wind speed for static wind instability in step 9) includes the following steps: first, draw the bridge structure deformation-wind speed curve according to the relationship between the bridge structure deformation and the wind speed, and then obtain the static wind speed according to the section with the largest slope in the curve. Instability critical wind speed.

Claims (6)

1. a method for static wind stability analysis of parallel double-width bridge, is characterized in that, comprises the steps: 1), construct numerical wind tunnel or physical wind tunnel model, then obtain the three-component force coefficient of upstream main girder and downstream main girder and the corresponding relationship of four parameters based on this model; Described three-component force coefficient comprises drag coefficient, lift coefficient and lift moment coefficient, the four parameters include the effective wind angle of attack α of the upstream girder, the effective wind angle of attack α' of the downstream girder, the torsion center distance d and the height difference h between the two girders; 2) Establish a spatial finite element model, including the information of the upstream bridge and the downstream bridge. The relative position relationship between the upstream bridge and the downstream bridge is consistent with the real bridge, and then solve the geometric nonlinearity under the action of self-weight; 3), set the initial wind speed V ₀ and the wind speed step size ΔV, the current wind speed V _i =V ₀ , and set the upper limit N _max of the number of iterations; 4) From the spatial finite element model, extract the torsion angle θ _i of each unit of the upstream main beam, the torsion angle θ _i ' of each unit of the downstream main beam, the center-to-center distance d _i and Height difference h _i ; 5) According to the torsion angle θ _i of each unit of the upstream main beam obtained in step 4), the torsion angle θ _i ' of each unit of the downstream main beam and the initial wind attack angle α ₀ , calculate the effective wind of each unit of the upstream main beam The attack angle α _i (=α ₀ +θ _i ) and the effective wind attack angle α _i '(=α ₀ +θ _i ') of each unit of the downstream girder; then according to the combination of four parameters (α _i ,α _i ',d _i , h _i ) Use the five-dimensional space interpolation method to calculate the three-component force coefficients of each unit of the upstream main beam and the downstream main beam; 6) Under the current wind speed V _i , calculate the lateral wind load P _Hi , vertical wind load P _Vi and torsional moment P _Mi acting on each unit of the upstream main girder, and the lateral wind load P _H ' of each unit of the downstream main girder _i , vertical wind load P _V ' _i and torsional moment P _M '_i; 7) Apply transverse wind loads P _Hi and P _H ' _i , vertical wind loads P _Vi and P _V ' _i , torsional moments P _Mi and P _M ' _i to each unit of the upstream main girder and downstream main girder respectively, Carry out the geometric nonlinear solution of the bridge structure, and obtain the torsion angle θ _i of each unit of the upstream main beam, the torsion angle θ _i ' of each unit of the downstream main beam, the torsion center distance d _i and For the height difference _hi above and below, judge whether the Euclidean norms of these four parameters are less than or equal to the allowable values ε ₁ , ε ₂ , ε ₃ and ε ₄ according to the following formula: In the formula, N is the total number of units of the main beam; k is the number of the current load step; i is the serial number of the beam unit; 8) If any of the above four formulas is not established, repeat steps 5)-7); if the number of iterations reaches the upper limit N _max of the number of iterations, it is difficult for the current wind speed to converge. At this time, the current wind speed V _i+1 =V _i - ΔV, then shorten the wind speed step, return to step 5), repeat steps 5)-7); if the wind speed step is less than the predetermined value, the calculation ends; if all the above four formulas are established, the current wind speed calculation result converges, and the calculation result is output , wherein the calculation result includes the deformation parameters of the bridge structure, at this time the current wind speed V _i+1 =V _i +ΔV, repeat steps 5)-7); 9), according to the calculation result obtained in step 8), obtain the critical wind speed and instability shape of the upstream bridge and the downstream bridge for static wind instability. 2. a kind of parallel double-width bridge static wind stability analysis method according to claim 1, is characterized in that, in described step 1), obtain the three-component force coefficient of upstream girder and downstream girder and the corresponding relationship of four parameters thereof The specific steps are as follows: the upstream main girder section and the downstream main girder section are simultaneously incorporated into the numerical wind tunnel or physical wind tunnel model, and the above four parameters are transformed to measure the three-component force coefficients under different combinations; The combination and the corresponding three-component force coefficients of the upstream and downstream main beam sections are stored in a callable array, and the corresponding relationship between the three-component force coefficients of the upstream main beam and the downstream main beam and their four parameters is obtained. 3. a kind of parallel double width bridge static wind stability analysis method according to claim 1, it is characterized in that, in described step 6), calculate and act on the horizontal wind load P _Hi of each unit of upstream girder, vertical wind load P The specific steps of _Vi and torsional moment P _Mi , and the transverse wind load P _H ' _i , vertical wind load P _V ' _i and torsional moment P _M ' _i of each unit of the downstream main girder are as follows: In the formula, C _Hi , C _Vi and C _Mi represent the drag coefficient, lift coefficient and lift moment coefficient of the upstream girder respectively; C' _Hi , C' _Vi and C' _Mi represent the drag coefficient, lift coefficient and lift moment coefficient; B represents the width of the main girder; l _i and l _i ' represent the lengths of the units of the upstream and downstream girders respectively; ρ is the air density; V _i is the current wind speed. 4. a kind of parallel double width bridge static wind stability analysis method according to claim 1, is characterized in that, in described step 2) and step 7), all adopt arc length method to carry out bridge structural geometrical nonlinear solution. 5. The static wind stability analysis method of a parallel double-width bridge according to claim 1, characterized in that the predetermined value of the wind speed step in step 8) is 0-0.5m/s. 6. a kind of parallel double width bridge static wind stability analysis method according to claim 1, it is characterized in that, in described step 9), the concrete steps of determining static wind instability critical wind speed are as follows: first according to the difference between bridge structure deformation and wind speed According to the relationship, the bridge structure deformation-wind speed curve is drawn, and then the critical wind speed of static wind instability is obtained according to the section with the largest slope in the curve.