JP4959359B2 - Bridge - Google Patents

Description

  The present invention relates to a bridge for wind resistance stability.

  When a bridge receives wind, divergent flexural vibration may occur due to the unique characteristics of the bridge. Since this vibration is self-excited vibration in which vibration energy is supplied by its own displacement, there is a risk of leading to collapse of the bridge.

As a countermeasure against vibration of the bridge, a method of standing a wall on the bridge girder upper surface that changes intermittently in the bridge axis direction (see, for example, Patent Document 1), installation of a wind-resistant addition member (for example, Patent Document 2, Patent) Reference 3), tuned mass dampers, etc. will be installed.
JP 9-21111 A Japanese Patent Laid-Open No. 9-125312 JP-A-11-269818

However, recent bridges tend to be longer spans and narrower, and it may be difficult to ensure the wind resistance of the bridges only with the above measures.
In addition, due to the recent trend of reducing public works costs, reduction of costs related to bridge construction is an essential issue, and it is difficult to secure a budget for taking new vibration control measures.
For the above reasons, it is necessary to design a bridge that ensures wind resistance stability from the initial design stage so that it is not necessary to take new vibration control measures for the existing bridge.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a bridge that can ensure wind resistance stability of the bridge while achieving cost reduction.

In order to solve the above problems, the present invention employs the following means.
In other words, the multi-span bridge according to the present invention has a bridge axis when the width of the envelope rectangle enclosing the outer shape of the cross section of the upper structure substantially orthogonal to the bridge axis direction of the bridge is B and the height is D. A superstructure in which the cross-sectional side length ratio B / D of the envelope quadrangle is changed with respect to the direction, and the superstructure has an upper structure divided body having the cross-sectional side length ratio B / D. The at least one upper structure divided body has a cross-sectional side length ratio B / D different from that of the other upper structure divided body, the lift coefficient of the upper structure is C _L , The angle between the average direction of the wind blown to the structure and the horizontal direction is α (positive in the blowing direction), the lift coefficient gradient is dC _L / dα, the nth span length from the end of the superstructure is L _n , lift the coefficient slope S _n, the maximum flexural vibration mode order in span and a _n In this case, the value of the expression (1) is 0 or more.

  By changing the cross-sectional side length ratio of the envelope rectangle with respect to the bridge axis direction, the wind resistance stability of the entire bridge can be improved, and the occurrence of divergent flexural vibration can be prevented.

By setting the value of equation (1) to 0 or more, the lift coefficient gradient dC _L / dα of the entire n-span bridge becomes 0 or more, and the occurrence of divergent flexural vibration can be prevented as a whole bridge. it can.
In this way, by ensuring the wind resistance stability by changing the span length of the bridge or the cross-sectional shape of the superstructure, it is not necessary to take new vibration control measures such as the installation of wind resistant additional members. Reduction can be achieved.

Furthermore, the multi-span bridge according to the present invention has a bridge girder having a cross section of a steel box girder.

  By adopting a bridge girder having a steel box girder cross section, the cost can be further reduced.

  By changing the span length or cross-sectional shape of the bridge, it is not necessary to take new vibration control measures such as the installation of a wind-resistant additional member, and it is possible to ensure wind-resistant stability and reduce costs.

[First Embodiment]
Hereinafter, an embodiment of a bridge according to the present invention will be described with reference to the drawings.
FIG. 1 is a side view showing a schematic configuration of a bridge according to the present embodiment.
The bridge 1 shown in the figure has an upper structure composed of a floor slab 2 and a bridge girder 3, and this upper structure includes a first upper structure divided body 4, a second upper structure divided body 5, 3 upper structure division bodies 6 are formed to be connected in the bridge axis direction.
FIG. 2 shows the cross-sectional shape of the second upper structural division body 5 that is substantially orthogonal to the bridge axis direction of the bridge.
The second upper structural division 5 shown in the figure includes a floor slab 2 and a bridge girder 3a extending in the bridge axis direction (the direction perpendicular to the paper surface). Further, when the width of the envelope rectangle enveloping the outer shape of the transverse cross section shown in the figure is B ₁ and the height is D ₁ , the section side length ratio of the envelope rectangle is expressed as B ₁ / D _1. .
FIG. 3 shows the cross-sectional shape of the first upper structural division body 4 and the third upper structural division body 6 that are substantially orthogonal to the bridge axis direction of the bridge.
The first upper structure divided body 4 and the third upper structure divided body 6 shown in the figure include a floor slab 2 and a bridge girder 3b extending in the bridge axis direction (direction perpendicular to the paper surface). Further, when the width of the envelope rectangle enveloping the outer shape of the cross section shown in the figure is B ₂ and the height is D ₂ , the section side length ratio of the envelope rectangle is expressed as B ₂ / D _2. .
Therefore, the upper structure of the bridge 1 shown in FIG. 1 includes a first upper structure divided body 4 having a cross-sectional side length ratio of B ₂ / D ₂ and a second upper structure having a cross-sectional side length ratio of B ₁ / D _1. The divided body 5 and the third upper structure divided body 6 having a cross-sectional side length ratio of B ₂ / D ₂ are connected and formed in the bridge axis direction.
Here, the cross-sectional side length ratio B ₁ / D ₁ of the second upper structural division body 5 is set smaller than the cross-sectional side length ratio B ₂ / D _{2 of} the first upper structural division body 4 and the third upper structural division body 6. Has been.

Next, the effect of the superstructure of the bridge formed by connecting the superstructure divided bodies having different cross-sectional side length ratios in the bridge axis direction will be described.
First, as a comparative example of the bridge according to the present embodiment, a single-span bridge having an upper structure whose cross-sectional side length ratio is constant with respect to the bridge axis direction is considered.
A bridge 7 shown in FIG. 14 is a single-diameter bridge having an upper structure with a cross-sectional shape shown in FIG. 2, and the cross-sectional side length ratio of the upper structure is B ₁ / D ₁ . FIG. 5 shows the relationship between the speed of the wind blown on the bridge and the amplitude of vibration generated in the bridge by the wind. According to FIG. 5, when the wind speed reaches a certain level or more, divergent flexural vibration in which the amplitude of the vibration increases rapidly is generated.
A bridge 8 shown in FIG. 15 is a single span bridge having an upper structure having a cross-sectional shape shown in FIG. 3, and the cross-sectional side length ratio of the upper structure is B ₂ / D ₂ . FIG. 6 shows the relationship between the speed of the wind blown on the bridge and the amplitude of vibration generated in the bridge by the wind. According to FIG. 6, even if the wind speed increases, no divergent flexural vibration in which the amplitude of the vibration increases rapidly is generated.

Next, for multi-span bridges with superstructures formed by connecting superstructure divisions with different cross-section side length ratios in the direction of the bridge axis, the wind speed of the wind blown on the bridge and the vibration generated in the bridge by the wind Consider the relationship with amplitude. Here, the bridge 1 shown in FIG. 1 is considered as an example.
FIG. 7 shows the relationship between the wind speed of the wind blown on the bridge and the amplitude of vibration generated in the bridge by the wind for the bridge 1 shown in FIG. According to FIG. 7, even if the wind speed increases, no divergent flexural vibration in which the amplitude of the vibration increases rapidly is generated. In other words, by connecting the bridge 7 between single diameters that was unstable to divergent flexural vibration and the bridge 8 between single diameters having wind resistance stability in the direction of the bridge axis, the wind resistance stability of the bridge as a whole. It has been shown that can be improved.
From the above, by ensuring the wind-resistant stability by changing the cross-sectional shape of the superstructure of the bridge, it is not necessary to take new vibration control measures such as the installation of wind-resistant additional members, and reduce costs. It is understood that is possible.

In the above embodiment, the cross-sectional shape shown in FIG. 3 has been described as an example of the cross-sectional shape substantially orthogonal to the bridge axis direction of the first upper structural division body 4 and the third upper structural division body 6. This invention is not limited to this, For example, the same effect can be show | played also as cross-sectional shape shown in FIG.
Moreover, in the said embodiment, although the shape of the cross section substantially orthogonal to the bridge-axis direction of the 1st upper structure division body 4 and the 3rd upper structure division body 6 was demonstrated as the same, this invention is limited to this. However, similar effects can be obtained even with different cross-sectional shapes.

Below, as one embodiment of the bridge according to the present invention, stability conditions for a three-span bridge will be described with reference to the drawings.
FIG. 8 is a schematic diagram illustrating a schematic configuration of a bridge according to the present embodiment.
The bridge 10 shown in FIG. 8 is a three-span bridge, and has an upper structure formed by connecting the upper structure divided body of the section A and the upper structure divided body of the section B in the bridge axis direction. Yes.
When the width of the envelope rectangle enveloping the outer shape of the cross section of the superstructure substantially orthogonal to the bridge axis direction of the bridge is B and the height is D, the section side length ratio of the envelope rectangle is expressed as B / D. Is done. In addition, when the lift coefficient of the bridge is C _L and the angle between the wind blown to the bridge and the horizontal direction is α, the bridge lift coefficient gradient S _c is derived as dC _L / dα to prevent divergent flexural vibration. For this, the value of the lift coefficient gradient S _c needs to be 0 or more.
Here, the span length of the upper structural division body of the cross section _A is represented as L ₁ , the cross section side length ratio is represented as (B / D) ₁ , and the lift coefficient gradient is represented as S _A. Further, the inter-span length of the upper structural division of the cross section _B is represented as L ₂ , the cross section side length ratio is represented as (B / D) ₂ , and the lift coefficient gradient is represented as S _B.
The span length L ₁ of the superstructure divided body of the cross section A and the maximum span length of the bridge 10, vibration mode function for each span is expressed as y = sin (π / L) x, per unit length of the superstructure Assuming that the cross-sectional shape in the bridge axis direction between each diameter is constant, the condition for preventing divergent flexural vibration as a whole of the bridge 10 is as follows: expressed.

As described above, divergent flexural vibration can be prevented as a whole of the bridge 10 by setting the design condition to satisfy the expression (2).
Therefore, when designing a three-span bridge having stability against divergent flexural vibration, a temporary determination of the cross section of the superstructure is first performed as shown in the flowchart of FIG. 9 (step S1 in FIG. 9). ), this superstructure ^{_{2S B (L 2 / L 1}} ) 3 + S value of _a makes a determination whether a 0 or more (in FIG. 9 step S2). At this time, when the value of ^{_{2S B (L 2 / L 1}} ) 3 + S A is less than zero, by the change of the cross-sectional shape or span length of the superstructure (in FIG. 9 step S3), and the whole bridge This will ensure the stability.

Below, the Example which applied the stability condition of the above-mentioned 3 span bridge concretely is described.
The bridge 15 shown in FIG. 10 is a three-span bridge, and has an upper structure formed by connecting an upper structure division body having a cross section A and an upper structure division body having a cross section B in the bridge axis direction. Here, the span length of the upper structural division body of the section A is provisionally determined to be L ₁ and the section side length ratio is 1.5. Further, the span length L ₂ of the upper structural division body of the section B is temporarily determined to be 0.8L ₁ and the section side length ratio is 2.0.
In the case of the above-mentioned cross section, from FIG. 11 where the test results obtained from the wind tunnel test are plotted, the cross section side length ratio B / D of the superstructure and the lift coefficient gradient dC _L / dα of the bridge are plotted. lift coefficient slope S _a superstructure split body -4.5, lift coefficient slope S _B of the superstructure division of section B is determined to be -3.1. Substituting these numerical values of L ₁ , L ₂ , S _A and S _{B into} the equation (2), the value on the left side of the equation (2) becomes −7.7, which is unstable with respect to the divergent flexural vibration. I know that there is.
Therefore, according to the flowchart of FIG. 9, the cross-sectional shape of the superstructure and the span length are redetermined to ensure stability against divergent flexural vibration. Here, the span length and the shape of the cross-section A are fixed, and the cross-sectional shape is restored so that the lift coefficient gradient S _B of the upper structural division of the cross-section _B is 4.4 or more as shown in the following equation (3). Do the design.

FIG. 11 is a graph plotting the test results obtained from the wind tunnel test with respect to the relationship between the cross-sectional side length ratio B / D of the superstructure and the lift coefficient gradient dC _L / dα of the bridge.
Using the figure, it is possible to simply obtain the required cross-sectional side length ratio in order to obtain a predetermined lift coefficient gradient.
In the bridge according to the present embodiment, it is read from FIG. 11 that the cross-section side length ratio should be 3.0 or more in order that the lift coefficient gradient of the superstructure divided body of the cross section B is 4.4 or more. be able to. That is, by changing the cross-sectional shape of the upper structural division body of the cross section B, it is possible to ensure wind resistance stability as the entire bridge 15.

As described above, according to the present embodiment, it is possible to prevent the occurrence of divergent flexural vibration as a whole of the bridge by changing the cross-sectional shape of some of the upper structural division bodies in the three-span bridge.
Therefore, by ensuring wind resistance stability by designing the bridge, it is possible to reduce costs without requiring new vibration control measures such as installation of wind resistant additional members.
In addition, in the said embodiment, although the design method which ensures stability by the shape change of the cross section B was demonstrated, this invention is not limited to this, Also by changing the length of a span or the cross section A, Similar effects can be obtained.

[Second Embodiment]
Below, 2nd Embodiment of the bridge concerning this invention is described with reference to drawings.
The bridge according to the present embodiment is different from the first embodiment in that the n-diameter bridge shows a stable condition against divergent flexural vibration.
A bridge 20 shown in FIG. 12 is an n-span bridge having an upper structure formed by connecting n upper structure division bodies. Here, the sectional shape of the n-th upper structure divided body from an end of the superstructure sectional n, span length L _n, lift coefficient gradient is represented as S _n, interval maximum mode A _n.
In this case, the vibration mode function between the diameters is expressed as y = sin (π / L) x, the mass per unit length of the superstructure is constant, and the cross-section with respect to the bridge axis direction between the diameters. Assuming that the shape is constant, the condition for preventing divergent flexural vibration as a whole of the bridge 20 is expressed by the following equation (4).

As described above, by setting the design condition to satisfy the expression (4), it is possible to prevent the divergent bending vibration from occurring as the bridge 20 as a whole.
Therefore, when designing an n-span bridge having stability against divergent flexural vibration, a temporary determination of the cross section of the superstructure is first performed as shown in the flowchart of FIG. 13 (step S11 in FIG. 13). ), Whether or not the upper structure satisfies the expression (4) is determined (step S12 in FIG. 13). At this time, if the expression (4) is not satisfied, the stability of the entire bridge is ensured by changing the cross-sectional shape of the upper structure or the span length (step S13 in FIG. 13).

  As described above, according to the present embodiment, it is not necessary to take new vibration control measures such as installation of wind resistant additional members by securing wind resistant stability by designing bridges for n-span bridges. It is possible to reduce the cost.

It is the side view which showed schematic structure of the bridge concerning this invention. It is front sectional drawing in the II cross section of the bridge shown in FIG. It is front sectional drawing in the II-II cross section of the bridge shown in FIG. It is front sectional drawing in the II-II cross section of the bridge shown in FIG. It is a figure showing the relationship between the wind speed of the wind which blows on a bridge about the single span bridge which has the upper structure of the cross section shown in FIG. 2, and the amplitude of the vibration which generate | occur | produces on a bridge by a wind. FIG. 4 is a diagram showing the relationship between the wind speed of the wind blown on the bridge and the amplitude of vibration generated in the bridge by the wind for the single span bridge having the upper structure of the cross section shown in FIG. 3. 2 for the multi-span bridge having an upper structure formed by connecting the upper structure divided body of the cross section shown in FIG. 2 and the upper structure divided body of the cross section shown in FIG. 3 in the bridge axis direction. It is a figure showing the relationship between the amplitude of vibration generated in the bridge by wind. It is the schematic which showed schematic structure of the bridge which concerns on 1st Embodiment. It is a flowchart showing the design procedure for preventing a divergent bending vibration about the bridge shown in FIG. It is the schematic which showed schematic structure of the bridge which concerns on an Example. It is the figure which plotted the test result obtained from the wind tunnel test about the relationship between the cross-section side length ratio of a superstructure, and the lift coefficient gradient of a bridge. It is the schematic which showed schematic structure of the bridge concerning 2nd Embodiment. It is a flowchart showing the design procedure for preventing a divergent bending vibration about the bridge shown in FIG. It is the side view which showed schematic structure of the single span bridge which has the upper structure of the cross section shown in FIG. It is the side view which showed schematic structure of the single span bridge which has the upper structure of the cross section shown in FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Bridge 2 Floor slab 3, 3a, 3b, 3c Bridge girder 4 1st upper structure division 5 2nd upper structure division 6 3rd upper structure division 7 Bridge 8 Bridge 10 Bridge 15 Bridge 20 Bridge 20

Claims (2)

When the width of the envelope quadrangle enveloping the outer shape of the cross section of the superstructure substantially perpendicular to the bridge axis direction of the bridge is B and the height is D,
With respect to the bridge axis direction, it has an upper structure in which the cross-sectional side length ratio B / D of the envelope rectangle is changed,
The upper structure is formed by connecting a plurality of upper structure divided bodies having the cross-sectional side length ratio B / D in the bridge axis direction,
At least one superstructure segment has a different cross-sectional side length ratio B / D with respect to other superstructure segments;
The lift coefficient of the superstructure is C _L , the angle between the average direction of the wind blown to the superstructure and the horizontal direction is α (positive in the blowing direction), and the lift coefficient gradient is dC _L / dα,
Wherein said n-th span length L _n from the end of the _{superstructure,} the lift coefficient slope S _n, the maximum flexural vibration mode order the when the A _n in span,
The multi-span bridge according to claim 1, wherein the value of the formula (1) is 0 or more.

The multi-span bridge according to claim 1, wherein the upper structure has a steel box girder cross section.

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