JP5014761B2 - Method for measuring tension of buried rod member - Google Patents

Description

  The present invention measures the tension of tie rods, tie wires, etc. embedded for the purpose of supporting concrete revetment structures in harbors, rivers, etc., and embedded rod members such as PC steel materials embedded in concrete structures (more precisely, The same applies hereinafter).

  When measuring the tension of a rod member such as a tie rod embedded in a concrete revetment structure or a PC steel member embedded in a concrete structure, the entire rod member is free space, such as a diagonal member of a cable-stayed bridge. There are significant difficulties compared to measuring the tension of structural members in

  For example, hitherto, the rod member was hit with a hammer or shaken with a hand, and the degree of tension was judged sensuously, but this method actually works. The tension cannot be grasped as an actual measurement value.

  Therefore, in order to accurately grasp the tension, the embedded rod member must be exposed over the entire length of the vibrating string. However, such a method is disadvantageous in terms of labor, time, and construction cost. large. In addition, when measuring the tension of PC steel material embedded in a concrete structure, the PC steel material and the concrete surrounding it constitute a structural material. It is often impossible to expose the length.

  In view of the above, the present inventors have conducted research on a method for measuring the tension of an embedded rod member such as an existing tie rod or an embedded PC steel in an embedded state by a simpler method, and have reached the present invention.

  First, the present inventors studied whether a vibration method known as a method for measuring the tension of an aerial cable or the like could be applied to the tension measurement of the rod member in the above example. As described in Non-Patent Documents 1 to 3 and Patent Document 1, the vibration method applies a shock to a cable in tension, detects vibration at an arbitrary point of the cable, performs frequency analysis, This is a method of measuring the cable tension by substituting the analysis result into a predetermined calculation formula prepared in the personal computer.

  Patent Document 1 is a technique for measuring the tension of wires in the air such as a cable laid on a bridge.

  It is known that a calculation formula derived from formula (I) described later is used for calculating the tension and the like.

  For example, Non-Patent Document 2 “Yamaguro Ichiro: Application of Simultaneous Estimation Method of Cable Tension and Bending Rigidity to Real Bridges” describes a calculation formula related to formula (I), which will be described later, based on actual measurement values. By substituting the following natural frequencies, "tension" and "bending stiffness" are estimated simultaneously. However, if it is actually applied, the boundary condition of vibration is not clear due to the cable end fixing condition or structure, etc.If the cable length and bending rigidity to be substituted into the calculation formula are not properly evaluated, the actual tension and In the non-patent document 3 “Bangyou-gai: A consideration on the cable cable tension measurement of PC cable-stayed bridges” in Non-Patent Document 3, the cable length and bending rigidity are compared by comparing the theoretical value with the actual measurement value. Consideration is being made.

Japanese Patent No. 3313028 Tetsuya Shinya “A practical calculation formula for cable tension by the vibration method” Proceedings of Japan Society of Civil Engineers, No. 294, pp. 25-32, February 1980 Ichiro Yamagoku “Application of Simultaneous Estimation Method of Cable Tension and Flexural Rigidity to Real Bridge” Annual Report of Steel Structure, Vol.5, 15-22, November 1997 Bunkai “A Study on Measurement of Tension Cable Cable of PC Cable-stayed Bridge” 54th Annual Scientific Lecture, Japan Society of Civil Engineers, 714-715, November 1999

The embedded rod member tension measuring method according to the present invention is to solve the following problems.
(1) Without exposing the vibration string length of the existing rod member in the embedded state such as an embedded tie rod or PC steel material, even if the numerical value of the vibration string length is unknown, there should be a limited exposure length If possible, make it possible to estimate the tension.
(2) The natural frequency can be measured by a simple method such as striking with a small hammer or the like, and can be performed in a short time.
(3) The above can be realized by a simple method of input and calculation using a personal computer.

  The present invention for solving the above problems has the following configuration.

1. Without exposing the vibration string length of an existing embedded rod member in an embedded state such as an embedded tie rod or PC steel material, even if the numerical value of the vibration string length is unknown, tension is applied from a limited exposure length. A method for measuring the tension of an embedded rod member to be measured,
A part of the length of the vibrating string of the rod member to be measured that can be vibrated is exposed by means such as excavation and suspension, a vibration sensor is disposed on the exposed part, and the exposed part is Vibrating by striking means such as a hammer, the natural frequency (f _i ) is obtained from the vibration detected by the vibration sensor, and the vibration mode order is determined from the relationship between the vibration mode order (i) and the natural frequency (f _i ). The square of (i) and the square of the natural frequency (f _i ) are expressed by a polynomial, and the apparent vibration chord length (L) of the rod member is obtained from a term corresponding to the fourth power of the vibration mode order (i). A method for measuring the tension of an embedded rod member, wherein the tension (T) is obtained from a term corresponding to the square of the vibration mode order (i).

2. Without exposing the vibration string length of an existing embedded rod member in an embedded state such as an embedded tie rod or PC steel material, even if the numerical value of the vibration string length is unknown, tension is applied from a limited exposure length. A method for measuring the tension of an embedded rod member to be measured,
A part of the length of the vibrating string of the rod member to be measured that can be vibrated is exposed by means such as excavation and suspension, a vibration sensor is disposed on the exposed part, and the exposed part is Vibrating by striking means such as a hammer, and measuring the natural frequency (f _i ) with a data logger for the vibration detected by the vibration sensor,
Giving the density (ρ) and cross-sectional area (A) of the rod member;
Giving a value of the bending stiffness (EI) of the rod member;
The vibration chord length (L) that is the length between the vibration end points of the rod member is calculated based on the natural frequency (f _i ), the density (ρ), the cross-sectional area (A), and the bending rigidity (EI). Ask
The rod member tension is calculated by substituting the natural frequency (f _i ), density (ρ), cross-sectional area (A), bending stiffness (EI), and vibration chord length (L) into the following formula (I). A method for measuring the tension of an embedded rod member, characterized in that

ここに、ｉ：モード次数
ｆ_i：モード次数に対応する固有振動数
ρ：密度
Ａ：断面積
Ｌ：振動弦長
ＥＩ：曲げ剛性
Ｔ：張力（軸力）

Where i: mode order
f _i : natural frequency corresponding to mode order
ρ: Density
A: Cross-sectional area
L: Vibration string length
EI: Flexural rigidity
T: Tension (axial force)

3. The least square approximation of the square value of the obtained natural frequency (f _i ) and the square value of the mode order (i) is performed, and the fourth order coefficient of the mode order (i) of the approximate curve is calculated. The method for measuring tension of an embedded rod member according to claim 1, wherein the vibration string length (L) is calculated.

4). The flexural rigidity (EI) is, in claim 3 quoting claim 2 or claim 2 characterized by using a value obtained from the Young's modulus of steel (E) a circular geometrical moment of inertia (I) A method for measuring the tension of the embedded rod member according to the description.
E = 2.0 × 10 ⁶ kg / cm ^{2
I = π × d 4/64} (cm 4)

  According to the tension measuring method for an embedded rod member according to the present invention, even if the vibration chord length of an existing rod member in an embedded state such as an embedded tie rod or PC steel material is unknown, a part of the embedded rod member is removed. Since the tension can be measured only by exposing it, and by a simple technique of hammering and input / calculation using a personal computer, the above-mentioned problems can be solved. In this specification, the “vibration string length” is the distance between the vibration end points, that is, the length of the entire rod member from one end to the other end of the rod member, excluding the length of the fixing portion by the anchor or the like. Say length.

  Hereinafter, the method for measuring the tension of the embedded rod member according to the present invention will be described in detail.

  The method for measuring the tension of the embedded rod member according to the present invention is such that the numerical value of the vibration string length is unknown without exposing the vibration string length of the existing embedded rod member in an embedded state such as an embedded tie rod or PC steel material. Even if it exists, tension | tensile_strength is measured from limited exposure length.

When measuring the tension of an embedded rod member whose vibration string length value is unknown, a portion of the vibration string length of the rod member that is the object of measurement can be vibrated and exposed by means such as excavation and suspension. A vibration sensor is disposed in the exposed portion, the exposed portion is vibrated by striking means such as a hammer, the natural frequency (f _i ) is obtained from the vibration detected by the vibration sensor, and the vibration mode order ( From the relationship between i) and the natural frequency (f _i ), the square of the vibration mode order (i) and the square of the natural frequency (f _i ) are expressed by a polynomial, which corresponds to the fourth power of the vibration mode order (i). The apparent vibration chord length (L) of the rod member to be obtained is obtained, and the tension (T) is obtained from the term corresponding to the square of the vibration mode order (i).

  More specifically, the calculation performed in the tension measurement is based on the following formula (I) which has been conventionally known.

ここに、ｉ：モード次数
ｆ_i：モード次数に対応する固有振動数
ρ：密度
Ａ：断面積
Ｌ：振動弦長
ＥＩ：曲げ剛性
Ｔ：張力（軸力）

Where i: mode order
f _i : natural frequency corresponding to mode order
ρ: Density
A: Cross-sectional area
L: Vibration string length
EI: Flexural rigidity
T: Tension (axial force)

  The above formula (I) is used when the tension (axial force) of the cable structure is measured by the natural frequency of the member, and is the vibration equation of the string or the bending vibration equation of the beam subjected to the tension. Are known. However, the vibration equation of the string is only the second term (tension term) on the right side of Equation (1), and the first term (rigidity term) on the right side is omitted. Further, the bending vibration law formula for a member to which no tension is applied has a form in which the second term (tension term) on the right side is omitted.

When obtaining the tension T, the second term (tension term) on the right side of the formula (I) is applied, and if the mode order (i) is omitted, the unknown (parameter) is (1) f _i : natural frequency, (2 ) Ρ: density, (3) A: cross-sectional area, (4) L: vibration string length, (5) EI: bending rigidity.

Of the above parameters,
(1) The natural frequency f _i is a numerical value obtained by actual measurement.
(2) The density ρ and (3) the cross-sectional area A are values determined by the member to be measured.
For example, the density ρ can be 7.85 kg / cm ³ , which is a general unit volume mass of iron, except when a special steel material such as stainless steel is used. In the case of special steel materials, a suitable unit volume mass is used. The cross-sectional area A can be obtained by actually measuring a member to be measured. Further, when a cross-sectional defect is caused by corrosion or the like, the value is used as it is when the ratio of the defect is small, and when the ratio of the defect is large, the value is appropriately adjusted to reflect the current state.
(5) As the bending rigidity EI, a value obtained from the Young's modulus E of the steel material and the circular second moment (I) is used.
E = 2.0 × 10 ⁶ kg / cm ^{2
I = π × d 4/64} (cm 4)
In addition, EI: bending rigidity is measured by selecting and cutting at least one sample at a position having the least influence even if it is cut at the site when there are many rod members to be measured, The bending stiffness TI can also be measured.
(4) L: The vibration string length is the length between the vibration end points, and is a value obtained from the coefficient of the stiffness term.
In the non-patent document 2 of Yamagaki et al. Described above, since the bending stiffness changes depending on the tension state of the cable, a method of simultaneously estimating the bending stiffness and the tension is adopted. In this method, the vibration string length (L) is a constant value, and for example, the length between fixed members such as a cable is used.

  However, as shown in the accompanying Non-Patent Document 3, in the vibration of the cable or the rod member, the vibration string length (L) is the fourth power in the first term (rigidity term) on the right side of the formula (I), The second term (tension term) is a square value, and fluctuations in the numerical value of the vibration chord length (L) have a greater effect on the rigidity or tension estimation results than fluctuations in other parameters. It has become. Therefore, as suggested by Yamagiwa et al., It seems that the elastic modulus (E) changes in the stress state and this needs to be estimated accurately. Determining the position and evaluating this as accurately as possible are important in measuring the tension, thereby avoiding the effect of fluctuations in the numerical value of the vibrating string length L on the tension measurement. The knowledge that it was possible was obtained.

  As is clear from the above, in the tension measuring method according to the present invention, the vibration chord length of the rod member to be measured does not need to be in free space, and if a part of the vibration chord length is exposed, the tension is not reduced. The feature is that measurement is possible. In other words, the numerical value of the vibration string length (L), which is an unknown number, is obtained by inputting (2) ρ: density, (3) A: cross-sectional area, and (5) EI: bending stiffness, and this numerical value is It will be possible to measure the tension (T). Thus, the vibration chord length (L), which is the distance between the vibration end points, can be obtained from the vibration measurement result for the position of the vibration end point that is difficult to evaluate, and as a result, the vibration chord length (L) can be directly measured. This means that it is not necessary to substitute the numerical value of the length of the exposed rod member (for example, about 5 meters in the embodiment described later) into the tension measurement formula.

  According to the tension measuring method according to the present invention, the length required for the actual measurement of the vibration frequency when the vibration chord length cannot be exposed, such as the PC steel material embedded in the concrete structure. The tension can be measured by exposing the PC steel material by, for example, a fishing operation.

  Next, the tension measuring method for the existing rod member according to the invention will be described in detail according to an embodiment.

  FIG. 1 is a configuration diagram showing an embodiment of a vibration measuring device used in the present invention, FIG. 2 is an explanatory diagram showing an example of the arrangement of the vibration measuring device of FIG. 1, and FIG. 3 is a graph and diagram showing an example of a frequency analysis result 4 is a graph showing an example in which 10 frequency analysis results are totaled and averaged, FIG. 5 is a graph showing an example of confirmation of the 5th and 6th order higher modes, and FIG. 6 is a 5th and 6th order. FIG. 7 is a graph showing an example of a high-order mode confirmation example, FIG. 7 is a graph showing an example of a plot of the square of the frequency and the square of the vibration mode order, and FIG. 8 is a graph showing an example of the least-square approximation.

  FIG. 1 shows the configuration of a vibration measuring device used when the present invention is implemented to measure the tension of an existing tie rod, and includes a vibration sensor (for example, an acceleration sensor) 10 and a data logger (for example, a dynamic strain measuring device). 20 and a personal computer 30, which are arranged in the field as shown in FIG.

  The vibration sensors 10 and 10 are fixed to the exposed tie rod 40 at an appropriate position in consideration of the tie rod length and the shape of each vibration mode. The fixing can be performed with an adhesive tape or the like, but the fixing means is not limited. It is preferable to use a plurality of vibration sensors 10 (two in this embodiment) in order to suppress measurement errors by avoiding overlooking the peak of the natural frequency. In addition, when a plurality of vibration sensors are used, the distance between the vibration sensors 10 and 10 is preferably fixed at an appropriate distance considering the shape of each vibration mode.

  As the vibration sensor 10, a known acceleration sensor can be used without any particular limitation.

  As the data logger 20, a known dynamic strain measuring instrument can be used without any particular limitation.

  The personal computer 30 records the data signal from the data logger 20, performs various calculations described below, and is used to display the results as numerical values and images.

  The above-described equipment is arranged on the site in the form shown in FIG. 2, but for the sake of easy understanding, description will be given with respect to the revetment site and tie rods.

  The base end of the tie rod 40 is fixed to the land side of the concrete revetment structure 41, the other end is fixed to the anchor 42, and is buried in the soil under a predetermined tension.

  The land side of the revetment structure 41 is excavated with a width of 5 m, for example, and the tie rod 40 is exposed (“exposed portion” shown in FIG. 2). The vibration string length of commercially available tie rods for revetment varies depending on the manufacturer and product number. For example, if the length of the entire tie rod 40 is 17.5 m and the fixed portions at both ends of the tie rod 40 are 50 cm each, the vibration string length is If it becomes 16.5m and 5m is exposed, the vibration string length of 11.5m will be in an embedded state in the ground.

  In addition, when substituting numerical values into the calculation formula described later, manufacturers of commercially available tie rods are limited (for example, Shinko Construction Materials Industry Co., Ltd., Nippon Tie Rod Industry Co., Ltd., Sogo Sangyo Co., Ltd., Tokyo Seimitsu Co., Ltd./ If the manufacturer name and product number of the tie rod 40 being used are clear from the design (construction) drawing or by visual inspection of the exposed tie rod 40, the numerical values may be substituted. In that case, it is preferable that the software prepared in the personal computer 30 is provided with a program in which necessary numerical values are substituted only by selecting a manufacturer name and a product number. More preferably, a program is provided for comparing with data obtained by actual measurement and taking measures in case of numerical mismatch.

  Next, the actual measurement will be described.

  First, the vibration sensor 10 is fixed at an arbitrary position of the exposed tie rod 40, hammering is performed at an arbitrary position away from the vibration sensor 10, and vibration is measured. The hammer hitting is preferably performed a plurality of times such as 10 times so as to generate vibrations in various vibration modes, and it is preferable to select an arbitrary position for each hit. Furthermore, in order to further improve the vibration measurement accuracy, it is also preferable to change the fixed position of the vibration sensor 10 and repeat hammering a plurality of times.

  When the collection of the vibration data is finished, the frequency is analyzed and the frequency corresponding to the mode order is read. Examples of frequency reading are shown in Table 1 and FIGS.

  Table 1 is a table obtained by reading the frequencies (Hz) corresponding to the respective vibration modes from the waveform of the frequency amplitude (micro μ) of the frequency analysis result as shown in FIG. When the peak of the dominant frequency is not clear, the average value processing shown in FIGS. 5 and 6 and the processing that makes the frequency stand out as shown in FIG. 7 are performed. FIG. 7 shows an example in which the frequency amplitude of each frequency analysis result is multiplied, but the dominant frequency is clear as compared with FIG.

  Next, the square values (shown in Table 2) of the obtained natural frequencies f and mode orders i are plotted as shown in FIG. 7, and the least squares are plotted as shown in FIG. The approximation is performed, and the vibration chord length (L) of the rod member is calculated from the coefficient of the fourth order of the mode order i of the approximate curve.

  When performing the least square approximation, the formula (I) is simplified as the following formula (II).

  From the result of the least square approximation, the following formula (III), which is an approximation formula, is obtained.

The vibration string length (L) is calculated from the α term of the formula (III).
That is, since a = 8.1924,

となり、Ｌ＝５．１２８（ｍ）が得られる。
ここで、
π＝３．１４
ＥＩ＝２．０８４（ｔｍ²）
ρ＝７．８５（ｔ／ｍ³）
Ａ＝１．１３４×１０^-3（ｍ²）

Thus, L = 5.128 (m) is obtained.
here,
π = 3.14
EI = 2.084 (tm ² )
ρ = 7.85 (t / m ³ )
A = 1.134 × 10 ⁻³ (m ² )

  In addition, it is necessary to consider gravity acceleration (g) in a calculation formula by the unit system used for calculation. Since the calculation uses a CGS unit system, the gravity acceleration (g) is applied to the molecule as described above. On the other hand, in the SI unit system, it is not necessary to multiply the gravitational acceleration (g) in which the gravitational acceleration is taken into consideration.

  In the tension measuring method for the existing rod member according to the present invention, the calculation performed by measuring the tension is based on the formula (I).

By substituting each value (mode order: i, natural frequency for the mode order i: f _i , density: ρ, cross-sectional area: A, vibration chord length: L, bending stiffness: EI) into the formula (I), Tension: T can be calculated.

By calculating the vibration string length (L) in the above, the tension (T) can be obtained from the coefficient b of the tension term.
That is, since b = 316.57,

となり、Ｔ＝３０．２２（ｔ）が得られる。ここで、単位ｔは引張を示す。

Thus, T = 30.22 (t) is obtained. Here, the unit t indicates tension.

  In order to verify the result of this example, measurement by the vibration method was performed. That is, when the distance between the gauge points of the amount of contraction of the rod member at the time of cutting the rod member was measured and simply verified, 10% of the value T = 30.22 (t) was obtained. A value of T = 34.5 (t), which is a margin of error, was obtained.

[Experimental example]
Hereinafter, an experimental example demonstrates the tension measurement method for an existing tie rod according to the present invention.

Experimental example 1:
A. The tie rod used was a commercial product having a total length of 17.50 m and a diameter of 38 mm (design value), and was embedded in a state where both ends were fixed (the fixed mounting portion was 50 cm each for both ends).
B. Tie rod digging (exposed)
About 5m, the minimum width required for the construction work, was excavated from the end of the buried tie rod, and the tie rod was excavated.
C. The bending stiffness (EI) of the tie rod was calculated.
D. The tie rod is excited by striking and the natural frequency of the tie rod is measured. The mode order is i, the natural frequency for the mode order i is f _i , the density is ρ, the cross-sectional area is A, the vibration string length is L, and the bending stiffness is Tension: T is calculated by substituting each value of EI into the formula.
E. It was found that the tension applied to each tie rod and the result of the tension (T) calculated by the tension measuring method of the present invention showed very close values.

The block diagram which shows one Example of the vibration measuring instrument used for this invention Explanatory drawing which shows the example of arrangement | positioning of the vibration measuring instrument of FIG. Graph showing an example of frequency analysis results Graph showing an example of summing up and averaging 10 frequency analysis results Graph showing an example of confirmation of fifth-order and sixth-order higher-order modes Graph showing an example of confirmation of fifth-order and sixth-order higher-order modes Graph showing an example of a plot of the square of the frequency and the square of the vibration mode order Graph showing an example of least square approximation

Explanation of symbols

10 Vibration sensor 20 Data logger 30 PC 40 Tie rod 41 Seawall structure 42 Anchor

Claims (4)

Without exposing the vibration string length of an existing embedded rod member in an embedded state such as an embedded tie rod or PC steel material, even if the numerical value of the vibration string length is unknown, tension is applied from a limited exposure length. A method for measuring the tension of an embedded rod member to be measured,
A part of the length of the vibrating string of the rod member to be measured that can be vibrated is exposed by means such as excavation and suspension, a vibration sensor is disposed on the exposed part, and the exposed part is Vibrating by striking means such as a hammer, the natural frequency (f _i ) is obtained from the vibration detected by the vibration sensor, and the vibration mode order is determined from the relationship between the vibration mode order (i) and the natural frequency (f _i ). The square of (i) and the square of the natural frequency (f _i ) are expressed by a polynomial, and the apparent vibration chord length (L) of the rod member is obtained from a term corresponding to the fourth power of the vibration mode order (i). A method for measuring the tension of an embedded rod member, wherein the tension (T) is obtained from a term corresponding to the square of the vibration mode order (i). Without exposing the vibration string length of an existing embedded rod member in an embedded state such as an embedded tie rod or PC steel material, even if the numerical value of the vibration string length is unknown, tension is applied from a limited exposure length. A method for measuring the tension of an embedded rod member to be measured,
A part of the length of the vibrating string of the rod member to be measured that can be vibrated is exposed by means such as excavation and suspension, a vibration sensor is disposed on the exposed part, and the exposed part is Vibrating by striking means such as a hammer, and measuring the natural frequency (f _i ) with a data logger for the vibration detected by the vibration sensor,
Giving the density (ρ) and cross-sectional area (A) of the rod member;
Giving a value of the bending stiffness (EI) of the rod member;
The vibration chord length (L) that is the length between the vibration end points of the rod member is calculated based on the natural frequency (f _i ), the density (ρ), the cross-sectional area (A), and the bending rigidity (EI). Ask
The rod member tension is calculated by substituting the natural frequency (f _i ), density (ρ), cross-sectional area (A), bending stiffness (EI), and vibration chord length (L) into the following formula (I). A method for measuring the tension of an embedded rod member, characterized in that

Where i: mode order
f _i : natural frequency corresponding to mode order
ρ: Density
A: Cross-sectional area
L: Vibration string length
EI: Flexural rigidity
T: Tension (axial force) The least square approximation of the square value of the obtained natural frequency (f _i ) and the square value of the mode order (i) is performed, and the fourth order coefficient of the mode order (i) of the approximate curve is calculated. The method for measuring tension of an embedded rod member according to claim 1, wherein the vibration string length (L) is calculated. The flexural rigidity (EI) is, in claim 3 quoting claim 2 or claim 2 characterized by using a value obtained from the Young's modulus of steel (E) a circular geometrical moment of inertia (I) A method for measuring the tension of the embedded rod member according to the description.

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