JP3115176B2 - Measurement method of natural frequency of bridge girder and spring constant of bearing - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring a natural frequency of a bridge and a method for measuring a spring constant at a support portion of the bridge.

[0002]

2. Description of the Related Art Conventionally, bridges in which abnormalities are observed by visual inspection are determined, and vibration is measured by applying an external force to them to measure natural frequencies and spring constants. In this case, there is a problem that the survey requires a lot of manpower and time, and the response to the external force includes the influence of the bearing portion and the foundation ground.

[0003]

In the measurement by the prior art, large-scale equipment is required for the measurement depending on the type and scale of the bridge, and the implementation requires considerable cost and labor. The point is that it is not possible to comprehensively investigate things. It also tries to solve the problem that the survey results are not always accurate.

[0004]

The predominant frequency of vibration at the center of the span is not the natural frequency of the bridge girder due to the influence of the bearing. For this reason, in the present invention, vibration data of a bridge is measured by installing sensors as shown in FIG. 1 not only at the center of the span but also at two places on the girder just above the bearing part and on the girder at the center of the span. By obtaining the ratio of the spectrum of the horizontal component and the spectrum of the vertical component of both measurement data, the dominant frequency excluding the influence of the bearing at each point can be obtained. Also, the spring constant of the bearing can be obtained from the obtained dominant frequency.

[0005]

[Operation] First, consider a simple girder in which the total mass m of the girder is concentrated at the center of the span. When the load P is applied to the center of the span, the deflection amount δ of the center of the span of this girder is given as follows.

[0006]

(Equation 1)

Here, L is the span length of the girder, E is the Young's modulus, and I is the second moment of area of the girder. The relationship between the amount of deflection δ at the center of the span and the natural circular frequency ω of the girder is given as follows, where g is the gravity constant.

[0008]

(Equation 2)

Consider a model in which a spar is supported by a spring at a support portion as shown in FIG. Here, the mass concentration coefficient e at the center of the span of the girder is given as follows.

(Equation 3)

For this reason, about 0.49 times the total mass of the girder is concentrated at the center of the span as the effective mass M2. Assuming that the effective masses at both ends are M1 and M3, and the vertical deflection amounts due to the dead load at both ends of the beam are respectively δ1 and δ3, the deflection amounts can be expressed as follows. Here, k1 and k3 are the spring constants of the upper and lower springs on the M1 side and the M3 side, respectively.

[0011]

(Equation 4)

[0012]

(Equation 5)

Since the amount of displacement at the center of the span includes the amount of subsidence of the bearing due to the weight of the girder and the amount of deflection of the girder itself, these two amounts must be distinguished. In the center of the span, the total displacement is δ2, and the deflection of the girder itself is δ
Assuming B, the total displacement δ2 at the center of the span can be expressed as follows.

[0014]

(Equation 6)

When the vibration of the girder is measured at the center point 2 of the span and the end point 1 (or end point 3), the dominant circular frequency ω2 of the spectral ratio of the vibration of the center point 2 of the span and the end point 1 (or end point 3) is obtained.
1 (or ω23) is expressed as follows.

[0016]

(Equation 7)

[0017]

(Equation 8)

Here, δ21 and δ23 can be respectively expressed as follows.

[0019]

(Equation 9)

[0020]

(Equation 10)

Thus, the deflection δB of the girder excluding the influence of both bearings is expressed as follows.

[0022]

[Equation 11]

Accordingly, the natural circular frequency ωB is obtained as follows.

[0024]

(Equation 12)

That is, the natural circular frequency ωB of the girder can be calculated from the predominant circular frequencies ω21 and ω23 of the spectrum ratio of the microtremor measured on the girder at the center of the span and on the girder immediately above both bearings. Thus, the natural frequency FB of the bridge girder can be obtained as follows.

[0026]

(Equation 13)

Further, from these results, the spring constants k1 and k3 of the two bearing portions can be calculated as follows. By the way, the relationship between each natural circular frequency and the natural frequency is F2 = ω2
/ (2π), F21 = ω21 / (2π), F23 = ω2
3 / (2π).

[0028]

[Equation 14]

[0029]

(Equation 15)

[0030]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Here, an embodiment in which the method of the present invention is applied to an actual bridge will be described. As shown in FIG. 3, this bridge consists of four main girder quadruples, and the superstructure is supported by rubber bearings. The span length is made equally for all four. FIG.
In the figure, the left bearing in the drawing is a fixed bearing, and the right bearing is a movable bearing.

In the measurement, fine movement was always measured simultaneously on the girder at the center of the span and on the girder immediately above the bearing. 100H for each measurement
4096 data were recorded three times by z sampling. In the frequency analysis, fast Fourier transform was performed on all 4096 data. The average of the three sets of results was used as the final Fourier spectrum. The spectral ratio was calculated for each measurement, and the three sets of results were averaged to obtain the final Fourier spectrum ratio. In this case, the minimum frequency resolution is about 0.024 Hz.

The measuring method and the analyzing method are not limited to the above methods.

FIGS. 4 to 7 show the obtained Fourier spectrum and spectrum ratio. From these peak frequencies,
Table 1 shows the results of calculating the natural frequency of the girder and the spring constant of the bearing. Formula based on these data

The natural frequency FB of the girder itself excluding the influence of the bearing portion of the girder calculated from Eq. (13) shows a stable value of 3.42 Hz to 3.45 Hz from the dominant frequency F2 at the center of the girder. .

[0034]

[Table 1]

[0035]

According to the present invention, no special measures are required for generating vibration at the time of measurement, and the measurement can be performed safely and easily simply by disposing the sensor at a predetermined position of the girder. it can. Post-processing of the measurement results is also easy, and the girder and the bearing can be quantitatively evaluated using the natural frequency and the spring constant. In addition, since the natural frequency of the girder and the spring constant of the bearing are analyzed based on the data measured at the same time, it is possible to greatly contribute to savings in cost and time.

[Brief description of the drawings]

FIG. 1 is a diagram showing a sensor installation position for measuring bridge vibration. (A) is a plan view, and (b) is a cross-sectional view.

FIG. 2A is a model diagram of a girder in which the mass of the girder is concentrated at the center of the span and both bearing portions, and FIG. 2B is a model diagram showing the amount of displacement of the girder and the bearing portion.

FIG. 3 is a schematic view of a bridge to which the present invention is applied.

4A and 4B of the embodiment, (a) the spectral ratio of horizontal vibration data at the end point of the fixed bearing and the center of the span, (b) the spectral ratio of horizontal vibration data at the end point of the movable bearing and the center of the span, (C) Spectral ratio of vertical vibration data at the end point of the fixed bearing side and the center of the span, (d) Spectral ratio of vertical vibration data at the end point of the movable bearing side and the center of the span, (e) Span affected by the bearing portion It is a figure which shows the spectrum of the vibration data in the center.

FIG. 5B is a diagram illustrating 2A of the embodiment: (a) the spectral ratio of horizontal vibration data at the end point of the fixed bearing side and the center of the span; (b) the spectral ratio of horizontal vibration data at the end point of the movable bearing side and the center of the span. (C) Spectral ratio of vertical vibration data at the end point of the fixed bearing side and the center of the span, (d) Spectral ratio of vertical vibration data at the end point of the movable bearing side and the center of the span, (e) Span affected by the bearing portion It is a figure which shows the spectrum of the vibration data in the center.

6A and 6B show: (a) the spectral ratio of horizontal vibration data at the end of the fixed bearing and the center of the span; (b) the spectral ratio of horizontal vibration data at the end of the movable bearing and the center of the span; (C) Spectral ratio of vertical vibration data at the end point of the fixed bearing side and the center of the span, (d) Spectral ratio of vertical vibration data at the end point of the movable bearing side and the center of the span, (e) Span affected by the bearing portion It is a figure which shows the spectrum of the vibration data in the center.

FIG. 7B is a view showing 4A of the embodiment, (a) the spectral ratio of horizontal vibration data at the end point of the fixed bearing side and the center of the span, (b) the spectral ratio of horizontal vibration data at the end point of the movable bearing side and the center of the span, (C) Spectral ratio of vertical vibration data at the end point of the fixed bearing side and the center of the span, (d) Spectral ratio of vertical vibration data at the end point of the movable bearing side and the center of the span, (e) Span affected by the bearing portion It is a figure which shows the spectrum of the vibration data in the center.

[Explanation of symbols]

1,3 Bridge pier 2 Bridge girder 4,5,6,7 sensor m total mass of g digit P load e mass concentration factor at center of girder g gravity constant L span length of girth E Young's modulus I second moment of area M1, Effective mass on both bearings of M3 girder (Fig. 2
(See (a)) M2 Effective mass applied to the center of the span of the girder (see FIG. 2 (a)) δ Deflection amount when the load P acts on the center of the span of the girder. 2 (b)) δ2 The total displacement at the center of the span (see FIG. 2 (b)) δ3 The subsidence amount of the bearing at point 3 (see FIG. 2 (b)) δB The girder at the center of the span (FIG. 2 (b))
Ω) Natural circular frequency when a load P acts on the center of the span ωB Natural circular frequency of the girder itself excluding the influence of the bearing ω21, ω23 Predominant circular frequency at each of the girder supporting parts FB The natural frequency of the girder itself excluding the influence F2 The dominant frequency of the girder affected by the bearing F21, F23 The dominant frequency of each girder bearing k1, k3 The spring constant of each girder bearing

Continued on the front page (72) Inventor Kazutoshi Hidaka 2-8-8 Hikaricho, Kokubunji-shi, Tokyo Inside the Railway Technical Research Institute (72) Inventor Masayuki Nishinaga 4-11-2 Takakura, Iruma-shi, Saitama 409 Examiner Jun Koriyama (58) Field surveyed (Int. Cl. ⁷ , DB name) G01H 17/00 G01M 13/00 G01M 19/00 JICST file (JOIS)

Claims (2)

(57) [Claims] In a method for measuring the natural frequency of a bridge girder, a sensor is installed at a point immediately above both bearings of a bridge girder and at a center of a span, and each of the sensors is installed at a point just above a bearing, Measure vibration data at the center point and at each point, and calculate the dominant frequency from the ratio of the spectrum of the vibration data measured at the point directly above the bearing and the vibration data measured at the center point between the supports. Calculate the dominant circular frequency at each point directly above the bearing from the dominant frequency and gravity constant at each point directly above the bearing, and calculate the center of the span from the calculated dominant circular frequency at the point directly above each bearing. Calculate the predominant circular frequency at the point, calculate the natural frequency at the center of the span from the calculated predominant circular frequency at the center of the span, and calculate the natural frequency at the center of the span between the calculated points. Characterized, measuring bridges digit natural frequency of the way that the natural frequency of the digits themselves Te. 2. A method for measuring a spring constant at a support portion of a bridge, wherein a sensor is installed at a point immediately above both support portions of the bridge girder and at a center point of the support, and a point just above each support portion and a point between the support portions are provided. Measure vibration data at the center point and at each point, and calculate the dominant frequency from the ratio of the spectrum of the vibration data measured at the point directly above the bearing and the vibration data measured at the center point of the span, and calculate Calculate the dominant circular frequency at the point directly above each bearing from the dominant frequency and the gravitational constant at each point directly above the bearing, and, on the other hand, calculate the distributed mass of the girder at the point directly above each bearing and at the center of the span. Calculate the effective mass to be replaced with the equivalent concentrated load at point, calculate the dominant frequency at each point directly above the bearing, and the calculated point just above each bearing and the center of the span between And effective mass of the natural frequency of the bridge according to claim 1, and calculates the spring constant of the support portion of the bridge from the method for measuring the spring constant of the bridge bearing.