JP2011047844A - Stress evaluation method and stress evaluation apparatus for piping structure - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a simple and accurate stress evaluation method of a piping structure for a so-called station piping which branches from a main pipe laid underground and has a plurality of inflection points on the ground. <P>SOLUTION: Assuming that a vertical directional displacement δ at an end of a branch pipe 9c is sum of a displacement δ1 caused by in-vertical-plane moment acting on the branch pipe 9c, a displacement δ2 caused by torsional deformation of a branch pipe 9b, and a displacement δ3 caused by bending moment of a branch pipe 9a toward the branch pipe 9b, a stress evaluation method of a piping structure evaluates a maximum stress σ arising in a piping structure using a following expression (10): the expression (10) is as follows: σ=ä3EGd<SB>o</SB>(2a+2b+c)δ}/äcG(12a<SP>2</SP>+12ab+4bc+10ca+c<SP>2</SP>)+3bc<SP>2</SP>E}, where a, b, c are length of the branch pipes 9a, 9b, 9c respectively, E is a vertical elastic coefficient, G is a horizontal elastic coefficient, d<SB>o</SB>is an outer diameter of the branch pipe, δ is a vertical directional displacement relative to the main pipe at a support part. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to an evaluation method and a stress evaluation apparatus for subsidence stress of a pipe structure which is a semi-buried establishment pipe branched from a main pipe buried in the ground and bent on the ground.

  Conventionally, in order to determine the stress generated in the buried pipe due to subsidence, the amount of subsidence of the buried pipe is measured at appropriate intervals, and the ground is replaced with a spring on the elastic floor where the ground is replaced with a spring. The stress distribution can be obtained by using a finite element method based on theory. In order to measure the subsidence amount of the buried pipe, a subsidence amount measuring jig called a subsidence rod is attached to the buried pipe, and the subsidence amount is measured.

  As such a stress analysis method, the buried pipe is modeled by a cylinder composed of shells, and the ground is modeled by connecting radial, tangential and axial springs to each intersection of a finite number of shell regions, There is a method of analyzing the displacement of these springs (Patent Document 1). There is also a method of obtaining stress by calculation by combining the settlement data with 3 or 4 points (Patent Document 2 and Patent Document 3).

Japanese Patent Laid-Open No. 09-269085 JP 2003-006180 A JP 2009-162296 A

  However, the conventional method such as Patent Document 1 has a problem that a considerable cost is required when it is used in a situation where the target location is not specified because the cost of study per case is extremely high. In addition, when Patent Documents 2 and 3 are used, it is difficult to evaluate stress for the following reasons in a so-called station pipe that has many rising branches and bent portions from the main pipe.

  First, the staff used for leveling of the side points when measuring the amount of subsidence measured the level values at three measurement points, for example, with the memory in increments of 5 mm and fixed transit at one location. In some cases, the maximum reading error between two points may be about 1 to 2 mm. However, since the station piping has a complicated shape, the interval between the measurement points may be 1 m or less. In this case, the yield point of the pipeline may be exceeded due to a reading error.

  In addition, when the methods such as Patent Document 2 and Patent Document 3 are used for the primary evaluation, man-hours are not required for the evaluation, but as a result of the evaluation, a stress far exceeding the actually generated stress is calculated. Will end up. Therefore, there is a need for a method for performing a simple primary evaluation before performing a secondary evaluation as in Patent Document 1 requiring man-hours for evaluation.

  In particular, as the primary evaluation, although it is a simple method, if the evaluation result is too biased toward the safety side, an unnecessary secondary evaluation is required as a result. It is necessary to evaluate the results as close as possible.

  The present invention has been made in view of such a problem, and is a simple and accurate stress evaluation method for a pipe structure for a so-called station pipe branched from a main pipe buried underground and having a plurality of bending points on the ground. The purpose is to provide.

In order to achieve the above-described object, the first invention includes a main pipe formed in a substantially horizontal direction and buried in the ground, a first branch pipe connected to the main pipe and rising in a substantially vertical direction, A second branch pipe provided on the ground and connected substantially vertically to the first branch pipe, and connected to the second branch pipe, and connected in a substantially horizontal direction and perpendicular to the second branch pipe. Stress evaluation method for a piping structure having a third branch pipe and a support part that supports the third branch pipe from below, wherein a vertical displacement δ of the support part is the third branch pipe. Displacement δ1 due to a vertical shearing force acting on the third branch pipe and a moment about the third branch pipe acting on the third branch pipe as a rotation axis in a direction perpendicular to and substantially horizontal to the third branch pipe, and the second branch pipe Displacement δ2 due to torsional deformation of the first branch pipe in the second branch pipe direction As the sum of the displacement δ3 by the bending moment, a stress evaluation method of the piping structure and evaluating the maximum stress σ generated in the piping structure with the formula (10).
σ = {3EGd _o (2a + 2b + c) δ} / {cG (12a ² + 12ab + 4bc + 10ca + c ² ) + 3bc ² E} (10)
However, a is the distance from the connection part with the main pipe in the first branch pipe to the second branch pipe connection part, b is from the connection part with the first branch pipe to the third branch pipe connection part. distance, c is the distance to the supporting portion from the connecting portion of the second branch pipe, E is Young's modulus, G is the modulus of transverse elasticity, d _o is the outside diameter of the branch pipe, [delta] of the main pipe in the support portion Relative vertical displacement.

  When the stress of the piping structure is calculated by the above-described stress evaluation method of the piping structure, and if the stress value is not more than a specified value, it is judged that the detailed stress evaluation of the piping structure is unnecessary, and the stress exceeds the specified value In this method, the displacement of each part of the piping structure is measured by a sinking bar attached to the distribution structure, and the detailed stress of the piping structure is obtained by a finite element method based on the displacement of each part obtained by the sinking bar. May be.

  According to the first aspect of the present invention, a main pipe formed in a substantially horizontal direction and buried in the ground, a first branch pipe connected to the main pipe and rising in a substantially vertical direction, and provided on the ground, A second branch pipe connected substantially vertically to the second branch pipe, and a third branch pipe connected to the second branch pipe and connected substantially horizontally and vertically to the second branch pipe. It is easy to measure the relative vertical displacement at the support part with respect to the main pipe for a complicated pipe structure that has a support part that supports the third branch pipe from below. Stress can be evaluated.

  Although the calculation result is slightly safer (about 20 to 30%) than the calculation result by FEM, it does not become an excessive evaluation result, so it can be used as a primary evaluation of a sufficient piping structure.

  If the stress evaluation of the piping structure is performed in detail by the secondary evaluation only in the case of a specified value (for example, 20% or more of the yield stress of the pipe) by the primary evaluation, the secondary evaluation may be performed only when necessary. Therefore, the evaluation man-hour can be significantly reduced.

According to a second aspect of the present invention, there is provided a main pipe formed in a substantially horizontal direction and buried in the ground, a first branch pipe connected to the main pipe and rising in a substantially vertical direction, and provided on the ground. A second branch pipe connected substantially vertically to the second branch pipe, and a third branch pipe connected to the second branch pipe and connected in a substantially horizontal direction and perpendicular to the second branch pipe. A stress evaluation device having a piping structure having a support portion for supporting the third branch pipe from below, and a distance from a connection portion with the main pipe in the first branch pipe to a second branch pipe connection portion. a, the distance b from the connection part of the first branch pipe to the third branch pipe connection part, the distance c from the connection part of the second branch pipe to the support part, and the longitudinal elasticity of each branch pipe coefficients E, and the transverse modulus of elasticity G, the outer diameter d _o of the branch pipe, but is input in advance, is stored in the storage means, Contact to the support portion By measuring δ, which is a relative displacement in the vertical direction with respect to the main pipe, and inputting it by the input means, the stress of the pipe structure is determined by the control unit according to the following equation (10) held in the storage means. When the calculated stress is equal to or less than a predetermined value, the control unit determines that the calculation is acceptable, and when the calculated stress exceeds the predetermined value, the control unit determines that the calculation is failed, and causes the display unit to display the calculation result. It is the stress evaluation apparatus of the piping structure characterized by this.
σ = {3EGd _o (2a + 2b + c) δ} / {cG (12a ² + 12ab + 4bc + 10ca + c ² ) + 3bc ² E} (10)

  According to the second invention, the main pipe formed in the substantially horizontal direction and buried in the ground, the first branch pipe connected to the main pipe and rising in the substantially vertical direction, and provided on the ground, the first A second branch pipe connected substantially vertically to the second branch pipe, and a third branch pipe connected to the second branch pipe and connected substantially horizontally and vertically to the second branch pipe. For a complicated piping structure in which a support part for supporting the third branch pipe from below is formed, by inputting only the relative displacement at the support part with respect to the main pipe, stress can be easily applied. Can be evaluated.

  According to the present invention, it is possible to provide a simple and accurate stress evaluation method for a pipe structure for a so-called station pipe branched from a main pipe buried underground and having a plurality of bending points on the ground.

The figure which shows the piping structure 1. FIG. The figure which shows (delta) 1 of piping structure. The figure which shows (delta) 2 of piping structure. The figure which shows (delta) 3 of piping structure.

  Hereinafter, embodiments of the present invention will be described in detail. FIG. 1 is a view showing a piping structure 1 according to the present invention. Under the ground 7, the main pipe 3 is embedded in a substantially horizontal direction. A main valve 5 is provided in the main piping.

  A branch pipe 9a is connected to the main pipe 3 in a substantially vertical direction. The branch pipe 9 a is extended to above the ground 7. A branch pipe 9b is connected to the end of the branch pipe 9a. The branch pipe 9b is connected in a direction substantially perpendicular to the branch pipe 9a. That is, the branch pipe 9b is provided in a substantially horizontal direction.

  A branch pipe 9c is connected to the end of the branch pipe 9b. The branch pipe 9c is substantially perpendicular to the branch pipe 9b and is connected in a substantially horizontal direction. A part of the branch pipe 9c is provided with a support portion 11 that supports the weight of the branch pipe from below. In the following description, the branch pipe 9c refers to a pipe from the connection part to the branch pipe 9b to the support part 11.

  The branch pipes 9a, 9b, and 9c have lengths a, b, and c, respectively. That is, the branch pipe 9a is installed in the vertical direction from the main pipe 3 to the height a, the branch pipe 9b is provided substantially vertically with respect to the branch pipe 9a and has a length b in the horizontal direction, and the branch pipe 9c is further provided in the branch pipe. A length c is provided vertically and horizontally in 9b, and the end of the branch pipe 9c is instructed from below by the support portion 11.

  In such a pipe structure 1, the highest stress is exhibited between the branch pipes 9 a and 9 b due to the sinking of the support portion 11 (sinking relative to the main pipe 3 or the main valve 5). Therefore, stress evaluation is performed in the range of the branch pipes 9a, 9b, and 9c.

  First, the piping structure 1 is modeled as shown in FIGS. 2-4 is the figure which looked at the piping structure 1 from the front, and the branch piping 9b becomes a direction (white circle in a figure) perpendicular | vertical to a paper surface. The lower end of the branch pipe 9a is a fixed end.

As shown in FIG. 2 (a), the bending (within the vertical plane) has a vertical shear force P acting on the branch pipe 9c and a direction substantially perpendicular to the branch pipe 9c acting on the branch pipe 9c as a rotation axis. Let the moment be M1. The vertical displacement of the branch pipe 9c end of this time the [delta] ₁ (Figure 2 (b)).

By the bending moment generated by the vertical shear forces P, calculated elastic strain energy _{U P} to be accumulated branch pipe 9a, 9b, 9c,, branch pipes 9a by the bending moment M1, 9b, the elastic strain energy _{U M1} accumulated in the 9c , the assumption based on the deflection angle corresponding to the bending moment M1 and zero at the position of the support portion 11, applying the theorem Kasuteriano, relationship between P and [delta] _1, the relationship between M1 and [delta] _1, respectively, wherein (1) and Equation (2).

P = {12EIδ ₁ (a + b + c)} / {c ³ (4a + 4b + c)} (1)
M1 = {12EIδ ₁ (a + b + c / 2)} / {c ² (4a + 4b + c)} (2)
However, E shows a longitudinal elastic modulus and I shows a cross-sectional secondary moment.

Next, as shown in FIG. 3A, the vertical displacement δ ₂ caused by the branch pipe 9c being twisted by the vertical shear force P and the bending moment M1 will be examined.

  The branch pipe 9b is twisted by a torsional moment (T1 in the figure) having a magnitude of (cP-M1) by the vertical shearing force P and the bending moment M1. Since the branch pipe 9c is joined to the branch pipe 9b, a displacement in the vertical direction is caused by the above-described torsional moment (FIG. 3B). The amount of vertical displacement δ2 at the end of the branch pipe 9c due to this torsional moment is expressed by equation (3).

_{δ 2 = {32 (cP-} M1) / (πd O 4 G)} · cb / e ··· (3)
However, G is a lateral elastic modulus and e is represented by Formula (4).

e = 1- (d _i ⁴ / d _O ⁴ ) (4)
However, _{d i} is the inner diameter of the branch pipes 9b, _{d O} denotes the outer diameter of the branch pipe 9a.

Equation (1) to P, M1 of the formula (3), by substituting equation (2), expressed the [delta] ₂ at [delta] ₁ can be expressed as Equation (5).

δ ₂ = {192bEI / πed _O ⁴ G (4a + 4b + c)} δ ₁ (5)

Next, as shown in FIG. 4A, when the branch pipe 9a is bent by the bending moment M2 (= cP-M1), the end of the branch pipe 9c transmitted to the branch pipe 9c via the branch pipe 9b. Consider the vertical displacement δ ₃ of.

The branch pipe 9c is displaced in the vertical direction as shown in FIG. 4B by the bending moment M2 of the branch pipe 9a. Equation (1), the equation (2), since it is M2 <M1, the use of M1 instead of M2 watching safety, [delta] ₃ is expressed as Equation (6).

δ ₃ = (ac / EI) M1 (6)

  Substituting equation (2) into equation (6) yields equation (7).

δ ₃ = {12a (a + b + c / 2) / c (4a + 4b + c)} δ ₁ (7)

  Here, assuming that the vertical displacement amount δ of the end portion of the branch pipe 9c is the sum of the above-described displacement amounts, δ is expressed by Expression (8).

δ = δ ₁ + δ ₂ + δ ₃ (8)

  The bending stress σ in the support portion 11 is expressed by the formula (9).

σ = M1 / z = M1d _O / 2I (9)
However, z shows a section modulus.

  As described above, when the bending stress σ is expressed by the displacement δ, the equation (10) is obtained.

σ = {3EGd _o (2a + 2b + c) δ} / {cG (12a ² + 12ab + 4bc + 10ca + c ² ) + 3bc ² E} (10)

  If Expression (10) is used, the length and outer diameter of the branch pipe and the strength of the branch pipe are set in advance, and only the vertical displacement amount (relative displacement amount with respect to the main pipe 3) in the support portion 11 is measured. Thus, the stress generated in the piping structure can be easily estimated.

  Therefore, input the equation (10), storage means such as a hard disk drive for storing various piping information and programs, etc., the CPU that is the control unit for performing various calculations and controls using equation (10), and the measurement values etc. Using a system (computer) having an input means such as a keyboard and a display means such as a display for outputting a calculation result, only the vertical displacement amount in the support portion 11 is measured, and the measurement result and branch piping information are input means The control unit reads out necessary information from the storage means and allows the system to calculate the stress value, thereby immediately knowing the stress value of the piping structure. Based on the measured stress value, if it exceeds the specified value, it can be rejected and the user can be informed (displayed etc.) to perform secondary evaluation. That. In this case, if various information (length, outer diameter, longitudinal elastic modulus, transverse elastic modulus, etc.) of the branch pipe is input in advance, stored in the storage means, and only measured δ is input, You may make it display a stress value and a pass / fail judgment.

  A comparison was made between the calculation result derived by the equation (10) and the analysis result by the detailed finite element method (FEM). The results are shown in Table 1.

  For comparison, the outer diameter of the pipe (outer diameter of the branch pipe) is 600 mm (outer diameter 60.96 cm, inner diameter 58.42 cm), and the outer diameter of the pipe (outer diameter of the branch pipe) is 300 mm (outer diameter 31. 85 cm, inner diameter 30.17 cm). The lengths a, b, and c of each branch pipe were all 200 cm, and the vertical displacement at the end of the branch pipe 9c was 1 cm. In addition, FEM analysis was analyzed about the two types, when the position which becomes a curved pipe part is regarded as joining of straight pipes, and when considered as a curved pipe.

  As is clear from Table 1, the FEM analysis result in the case of a straight pipe almost coincided with the calculation result according to the present invention. Moreover, the calculated value of this invention showed the value of the somewhat safe side (high stress). Similarly, in the FEM analysis result in the case of a curved pipe, the stress concentration coefficient and the deflection coefficient are taken into consideration, and a lower stress value is shown. However, according to the method of the present invention, it is 2-3. We were able to get an evaluation on the safe side.

  As described above, according to the method of the present invention, the stress value of the station piping structure can be easily obtained. The obtained value is a value on the safe side with respect to the actual value (FEM analysis value), and the difference is about 20 to 30%. For this reason, for example, when the evaluation according to the present invention is a primary evaluation and the evaluation value is within a specified value (for example, less than 20% of the yield stress of the branch pipe), it is determined that there is no problem, and the evaluation value exceeds the specified value. In such a case, if more detailed evaluation (secondary evaluation) is performed, there is no need to perform unnecessary secondary evaluation, and efficiency is improved.

  In addition, since the actual measurement point is only the vertical displacement at the support portion, the measurement is easy. It should be noted that, for example, conventionally proposed Patent Document 2 and Patent Document 3, such as the embedded section formula, the exposed section formula, and the formula of the boundary between the buried section and the exposed section are converted into a three-dimensional piping structure as in the present case. When applied, the evaluation result on the safety side is about 10 times the FEM analysis result described above. For this reason, as a primary evaluation method, by using the expression (10) based on modeling and various assumptions according to the present invention, appropriate evaluation can be performed without looking at an excessive safety factor.

  As mentioned above, although embodiment of this invention was described referring an accompanying drawing, the technical scope of this invention is not influenced by embodiment mentioned above. It is obvious for those skilled in the art that various modifications or modifications can be conceived within the scope of the technical idea described in the claims, and these are naturally within the technical scope of the present invention. It is understood that it belongs.

DESCRIPTION OF SYMBOLS 1 ......... Piping structure 3 ......... Main piping 5 ......... Main valve 7 ......... Ground 9a, 9b, 9c ......... Branch piping 11 ......... Support part

Claims (3)

A main pipe formed in a substantially horizontal direction and buried in the ground;
A first branch pipe connected to the main pipe and rising in a substantially vertical direction;
A second branch pipe provided on the ground and connected substantially perpendicularly to the first branch pipe;
A third branch pipe connected to the second branch pipe and connected in a substantially horizontal direction and perpendicular to the second branch pipe;
A support portion for supporting the third branch pipe from below;
A stress evaluation method for a piping structure having
The vertical displacement δ of the support is
A vertical shear force acting on the third branch pipe and a displacement δ1 due to a moment about a direction perpendicular to and substantially horizontal to the third branch pipe acting on the third branch pipe as a rotation axis;
Displacement δ2 due to torsional deformation of the second branch pipe;
A pipe characterized in that the maximum stress σ generated in the pipe structure is evaluated by the equation (10), assuming that the sum is a displacement δ3 due to a bending moment of the first branch pipe in the second branch pipe direction. Structural stress evaluation method.
σ = {3EGd _o (2a + 2b + c) δ} / {cG (12a ² + 12ab + 4bc + 10ca + c ² ) + 3bc ² E} (10)
However, a is the distance from the connection part with the main pipe in the first branch pipe to the second branch pipe connection part, b is from the connection part with the first branch pipe to the third branch pipe connection part. distance, c is the distance to the supporting portion from the connecting portion of the second branch pipe, E is Young's modulus, G is the modulus of transverse elasticity, d _o is the outside diameter of each branch pipe, [delta] is a main pipe in the support portion Relative vertical displacement. The stress of the piping structure is calculated by the stress evaluation method of the piping structure according to claim 1,
If the stress value is less than or equal to a specified value, it is determined that the detailed stress evaluation of the piping structure is unnecessary,
When the stress exceeds a specified value, the displacement of each part of the piping structure is measured by a sinking rod attached to the distribution structure,
A stress evaluation method for a piping structure, characterized in that a detailed stress of the piping structure is obtained by a finite element method based on the displacement of each part obtained by the sinking rod. A main pipe formed in a substantially horizontal direction and buried in the ground, a first branch pipe connected to the main pipe and rising in a substantially vertical direction, and provided on the ground and substantially perpendicular to the first branch pipe A second branch pipe connected to the second branch pipe, a third branch pipe connected to the second branch pipe substantially horizontally and perpendicular to the second branch pipe, and the third branch A stress evaluation device for a pipe structure having a support part for supporting the pipe from below,
A distance a from the connection with the main pipe to the second branch pipe connection in the first branch pipe; a distance b from the connection with the first branch pipe to the third branch pipe connection; and the distance c from the connection portion between the second branch pipes to the support part, longitudinal elastic modulus E of each branch pipe, and the transverse modulus of elasticity G, the outer diameter d _o of the branch pipe, but is input in advance, in the storage means By storing δ, which is a displacement in the vertical direction relative to the main pipe in the support portion, and inputting it by the input means, the following equation (10) held in the storage means: The piping unit stress is calculated by the control unit, and the control unit determines that the calculated stress is less than or equal to a predetermined value, and determines that the calculated stress exceeds a predetermined value. A stress evaluation device for a piping structure, wherein a calculation result is displayed on a display means.
σ = {3EGd _o (2a + 2b + c) δ} / {cG (12a ² + 12ab + 4bc + 10ca + c ² ) + 3bc ² E} (10)

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