JP2008051637A - Method for measuring bending stress of fixed structure, recording medium, and computer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a bending stress measuring method which is simple and is capable of exactly measuring even a local stress, and a recording medium recorded with a program for performing the method, and a computer for performing the method. <P>SOLUTION: A separation distance from the surface of a fixed structure up to the position of a neutral axis is calculated (S2); by adding this value to an actually measured distance value acquired by an actually distance measuring process (S1), the length of the neutral axis is calculated by the use of an angle looked from a measurement reference position or the distance value of a measurement interval (S3); an initial position of the neutral axis in a state that external force does not act is calculated from a position corresponding to the total sum value of length values of the neutral axis and the magnitude of an initial curvature, to find a displacement quantity (S5); a variation in the curvature is found by differentiating the displacement quantity (S8); and a stress intensity is acquired by multiplying this variation by the elastic modulus of the fixed structure and its geometrical moment of inertia to calculate a bending moment, and dividing it by a section modulus (S10). Moreover, an external load is found from a relation in balance between force and moment at a minute part on the neutral axis (S12). <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for measuring a bending stress of a fixed structure for measuring a bending stress generated in a fixed structure such as a water pipe or a tunnel structure, a recording medium on which a program for executing the method is recorded, and the method Related to computers.

  In Patent Document 1, a proportional relationship between the flattening amount of the pipe (the amount of change in outer shape) and the circumferential maximum stress is obtained in advance by experiment, and the flattening amount of the curved pipe is measured with a tool such as a caliper from two directions. Calculate the flattening amount of the curved pipe, calculate the in-plane bending moment and the out-of-plane bending moment separately from the relational expression between the flattening amount and the moment of the bending pipe, and apply a predetermined logical formula from these moments to calculate the stress. It is disclosed to calculate the distribution.

  On the other hand, in Patent Document 2, a magnetostrictive sensor is run along the inner peripheral surface or outer peripheral surface of a pipe material, the magnetostriction is measured at a number of positions continuous in the pipe circumferential direction, and the measured value of magnetostriction is approximated by a SIN2θ curve. Thus, it is disclosed that the stress distribution is calculated.

JP 2003-344184 A Japanese Examined Patent Publication No. 7-69226

  However, in the technique of Patent Document 1, it is necessary to obtain the relationship between the flattening amount of the bent pipe and the stress through experiments, and it is difficult to accurately calculate the stress acting locally on the peripheral surface of the pipe. is there. In particular, in the case of a large-diameter pipe having a pipe diameter of 1 m or more, it is difficult to obtain the relationship between the flattening amount and the stress through experiments.

  In Patent Document 2, it is necessary to travel the magnetostrictive sensor along the peripheral surface of the pipe material, and there is a problem that installation of the travel rail and the travel device becomes complicated. Further, since the measurement point is approximated to SIN2θ, there is a possibility that a value at a location where a large stress is locally generated may be removed, and there is a problem that accurate stress measurement is lacking.

  Therefore, the present invention provides a method for measuring the bending stress of a fixed structure that can easily and accurately measure a local stress, a recording medium on which a program for executing the method is recorded, and a computer for executing the method. It is aimed.

  In order to solve the above-mentioned problem, the invention described in claim 1 is directed to the surface of the fixed structure continuously from an arbitrary measurement reference position at an appropriate interval from the surface of the fixed structure on which an external force is applied. Measured distance measurement process that measures the distance to multiple measurement positions and obtains multiple continuous measured distance values, and calculates the separation distance from the surface of the fixed structure to the neutral axis position. The distance from the measurement reference position to the neutral axis of the fixed structure is added to the actual measurement distance value obtained in step 1, and these values for the adjacent measurement points and the distance from the measurement reference position or the distance of the measurement interval Based on the measured neutral axis position calculation process that calculates the length of the neutral axis using and the neutral axis length obtained from the measured neutral axis calculation process, the position corresponding to the cumulative value of this length and the initial External force is acting due to the magnitude of curvature Displacement calculation for determining the displacement at each measurement position of the fixed structure from the difference between the measured neutral axis position and the initial neutral axis position, and the initial neutral axis calculation process for calculating the initial position of the neutral axis of the fixed structure The bending moment is continuously calculated by differentiating the process and the displacement at each measurement position to determine the amount of change in curvature at each measurement position, and multiplying this by the elastic modulus of the fixed structure and the secondary moment of inertia. The bending moment calculation step, the stress calculation step to obtain the degree of stress at the measured distance measurement position by dividing the moment value obtained in the bending moment calculation step by the section modulus, and the minute part on the neutral axis of the fixed structure Establish simultaneous equations based on the balance between force and moment, and start from the intersection with the axis end or axis of symmetry where initial conditions can be set, and then continue sequentially along the neutral axis Characterized by and an external load calculating step of calculating an external load applied to the axis of the neutral axis by solving the simultaneous equations.

  The invention described in claim 2 is the invention described in claim 1, wherein the fixed structure has an arc shape, and the actual distance measuring step is installed at a measurement reference position inside the fixed structure. The distance from the measurement reference position to the surface of the fixed structure is measured at a continuous angle by a rotary laser distance measuring machine.

  The invention described in claim 3 is the invention described in claim 2, characterized in that the fixed structure is a tubular body embedded in the ground.

  According to a fourth aspect of the present invention, in the first aspect of the present invention, the fixed structure has a linear shape, and the measurement reference position in the actual distance measurement step is arbitrary along the surface of the fixed structure. Each distance from the measurement reference line to the surface of the fixed structure is measured by a scanning laser distance measuring device that travels on a rail installed on the measurement reference line.

  According to a fifth aspect of the present invention, in the first aspect of the invention, in the measured neutral axis position calculating step and the displacement calculating step, the measured distance or the amount of displacement is Fourier-transformed, and these values are averaged. And after making the change into a smooth curve, it differentiates.

  The invention described in claim 6 is the invention described in claim 1, wherein the fixed structure does not form a ring and has an end, and the measured distance or displacement from the end to an arbitrary position. By connecting, at the end portion, a curve obtained by reversing the change curve on the graph, a virtual curve that is continuous at the end portion and periodically changes every double length is differentiated.

  The invention described in claim 7 is the invention described in claim 2, wherein the fixed structure is a circular tube, and the cosine theorem is obtained with respect to the distance and angle of each measurement point obtained in the actual distance measurement step. The center length before the fixed structure is deformed is calculated by dividing the circle of the obtained shape into two parts in the vertical direction and the horizontal direction, and the measurement is performed at the time of measuring the center position and the distance. After calculating the deviation from the reference position, a centering step of converting the actually measured distance data into a distance from the center position is provided.

  According to the eighth aspect of the present invention, there is provided an arbitrary structure having an appropriate distance from the surface of the fixed structure on which an external force is applied to a fixed structure in which the axis of the neutral axis has an arbitrary shape. Measure the distance from the measurement reference position to multiple continuous measurement positions on the surface of the fixed structure to obtain multiple continuous measured distance values, and the distance from the fixed structure surface to the neutral axis position. By calculating the separation distance and adding this to the actual distance value obtained in the actual distance measurement process, the distance from the measurement reference position to the neutral axis of the fixed structure is obtained. Based on the measured neutral axis position calculation process that calculates the length of the neutral axis using the angle or the measurement interval distance value viewed from the reference position, and the neutral axis length obtained from the measured neutral axis position calculation process , The position corresponding to the cumulative value of this length Using the initial neutral axis curvature data reading process to obtain period curvature data, and using the initial curvature data obtained in these processes and the measured neutral axis position data, the change in the neutral axis curvature caused by the load is calculated. Further, by calculating the curvature and bending moment based on the neutral axis distance data for calculating the bending moment and dividing the moment value obtained in the bending moment calculation step by the section modulus, the degree of stress at the measured distance measurement position is obtained. In a small part on the neutral axis of the fixed structure in the stress calculation process, a simultaneous equation is established from the relationship between the balance of force and moment, and the neutral axis starts from the intersection of the axis end or axis of symmetry where initial conditions can be set. An external load calculation step for obtaining an external load acting on the axis of the neutral axis by solving simultaneous equations sequentially along To.

  The invention described in claim 9 is a recording medium on which a program for performing the process according to any one of claims 1 to 8 is recorded.

  A tenth aspect of the present invention is a computer that executes the program according to the ninth aspect.

According to the first aspect of the present invention, in the fixed structure on which an external force is applied, the stress acting on the fixed structure only by the actually measured distance to the measurement position on the surface of the fixed structure measured by the actually measured distance measuring step. Can be easily measured.
In general, the bending stress σ has the relationship of the following first formula.

また、モーメントＭと曲率の変化ΔΦとの間には、下記第２式の関係がある。

Further, there is a relationship of the following second formula between the moment M and the curvature change ΔΦ.

ΔΦについては下記の第３式及び第４式から得ることができる。

ΔΦ can be obtained from the following third and fourth equations.

(1) The measurement reference position moves along a line, and the displacement v _{i at the} measurement position is measured as an offset of the equal interval Δx along the measurement reference line (see FIG. 14).

In particular, the simplified standard formula for straight beams and the like is as follows. However,
The measurement reference line (measurement reference position) is parallel to the original neutral axis.

(2) The measurement reference position is a fixed point, and the displacement w _i is measured at the measurement reference point at an equal angle Δψ (see FIG. 3).

特に、円環に関して簡略化された標準式は次のようである。

In particular, a simplified standard formula for an annulus is as follows:

  In claim 8, the method of directly obtaining the curvature from the measured distance measurement result is as follows.

(1) When using distance data y _i measured as an offset of equal intervals Δx along the measurement reference line (see FIG. 14)

（２）測定基準点において等角度Δψで測定した距離データｌ_iを用いる場合（図３参照）

(2) When using distance data l _i measured at the equiangular angle Δψ at the measurement reference point (see FIG. 3)

  As is apparent from the above equation, the curvature is obtained by differentiating the length (distance). However, since the actual measurement value includes an error, a correct solution cannot be obtained by differentiating it as it is. Therefore, this problem is solved by applying the Fourier transform in claim 5 to average the measured values and smooth the change. In other words, the following equation is used to convert displacement or distance equal length data into a Fourier-class mathematical expression, so that not only the average value of the data but also the differential coefficient obtained when it is differentiated can be obtained. It is what.

  According to the present invention, the distance from the measurement reference position to the structure surface is continuously measured at a plurality of locations (actual distance data) to determine the curvature of the neutral axis, and by calculating the difference from the original curvature, The change in curvature at the measurement point is obtained. Therefore, since the measurement only measures the distance from the measurement reference position to the surface of the fixed structure, it is only necessary to have a distance measuring device, which is extremely simple.

  In the sixth aspect of the invention, the method for enabling the Fourier transform to be applied to a non-periodic variable is specifically as follows. In this case, the variable can be either Li = f (ψi) expressed in polar coordinates or Yi = f (xi) expressed in rectangular coordinates (see FIG. 14).

A group of stations on the neutral axis indicated by the variable is developed on one orthogonal coordinate, and its start point is A and its end point is B. By the translation and rotation method, the coordinate transformation is performed so that A is set on the origin of the coordinate system and B is set on the coordinate axis without changing the shape of the neutral axis. Let these be A ₀ and B ₀ , respectively. Making A ₁ -B ₁ and A ₀ -B ₀ and the B ₀ at the center is rotated 180 degrees. As a result, the neutral axis as a whole becomes A ₀ -B ₀ / A ₁ -B ₁ . A ₀ -B ₀ and A ₁ connecting point B ₀ / B ₁ of -B ₁ is smooth and differentiable.

Next, the _{A 0 -B 0 / B 1 -A} 1 around the A ₁ is rotated 180 degrees, making _{A 2 -B 2 / B 3 -A} 3. As a result, the neutral axis as a whole becomes A ₀ -B ₀ / B ₁ -A ₁ / A ₂ -B ₂ / B ₃ -A ₃ . _{A 0 -B 0 / B 1 -A} 1 and A ₂ -B ₂ / B ₃ connecting point A ₁ / A ₂ of -A ₃ is smooth and differentiable.

The virtual neutral axis A ₂ -B ₂ / B ₃ -A ₃ added by the above operation can also be obtained by translating the initial neutral axis A ₀ -B ₀ / B ₁ -A ₁ along the coordinate axis. That is, A ₀ -B ₀ / B ₁ -A ₁ / A ₂ -B ₂ / B ₃ -A ₃ are A ₀ -B ₀ / B ₁ -A ₁ and A ₂ -B ₂ / B ₃ -A ₃ Are two-cycle variables, each of which is a cycle. Therefore, if the length 2π of the section A ₀ -B ₀ / B ₁ -A ₁ is taken, the Fourier transform for the periodic variable of the ninth equation can be applied as it is. Of the Fourier series obtained by this equation, the section corresponding to A ₀ -B ₀ , that is, between 0-π, is obtained by subjecting the target non-periodic variable to Fourier transform. According to this method, the curvature can be obtained reasonably and without deviation up to the end of the corresponding section.

The external load calculation step of claim 1 is based on the following formula.
Taking a minute section on the neutral axis of the fixed structure, assuming the end point as 1 and the end point as 2, and assuming the end face perpendicular to the neutral axis at those points, the direction of each surface and the force generated on each surface And moment (internal force) are expressed as follows.

  In addition, between 1 and 2, it is assumed that the applied load (external force) acts at right angles and parallel to the neutral axis, and is expressed as follows.

In this simultaneous equation, the bending moments at both ends of each minute section are known by the bending moment calculation process shown here, and the initial value is appropriately set by actual measurement or estimation at a singular point such as the neutral axis end or the symmetric axis on the neutral axis. If it can be set, it can be solved continuously by sequentially replacing the starting point 1 and the ending point 2. However, since there are three equations, the number of unknowns is limited to three. Since two of them need to be assigned to N ₂ and Q ₂ , there is a restriction that only the remaining one can be used for external loads.

In this case, depending on the situation,
(1) P _m is calculated with T _m = 0.
(2) Assuming a vertical load intensity u and a horizontal load intensity v, u is known and v is solved.
There are methods. In either case, a practically sufficient solution can be obtained. In particular, if this method is applied to buried pipes, the “passive resistance coefficient (N / mm ² )” and “ground coefficient (N / mm ² / mm)” of the soil can be easily obtained.

  Since the distance measurement is for knowing the displacement of the neutral axis of the fixed structure or the shape thereof, the installation position of the distance measuring device can be arbitrarily determined if this purpose can be achieved. In particular, in the case of a fixed structure with a neutral shaft closed, the original center position can be obtained by the centering method according to the seventh aspect, so that the displacement can be easily calculated.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. First, the first embodiment will be described with reference to FIGS. FIG. 1 is a block diagram showing a configuration of a computer that performs bending stress / loading load measurement according to the present embodiment, FIG. 2 is a flowchart executed by the computer according to the present embodiment, and FIG. 3 is a fixed structure. FIG. 4 is a cross-sectional view for explaining an actual distance measurement process in the case where is a circular pipe, and FIG. 4 is a diagram showing a distance measurement from the measurement reference position to the surface of the circular pipe (fixed structure) in the actual distance measurement, And a method (centering) for converting a measurement result from the distance measuring device into a value from the center position of the circular pipe (centering). FIGS. 5 to 10 are analysis graphs of a computer in each step.

  As shown in FIG. 3, the fixed structure 1 according to the embodiment of the present invention is a steel pipe having a circular cross section, and has a radius of about 1 m. The fixed structure 1 is a water pipe and is buried in the ground to flow irrigation water or the like.

  The distance measuring device 3 is a laser distance measuring device, and the laser tube 4 sequentially emits laser light starting from the intersection with a vertical line or a horizontal line at every angle obtained by equally dividing the entire circumference 360 degrees (for example, 500 divisions). Measure the distance to the inner surface of the tube. The laser distance measuring device 3 measures the distance from the laser transmitter 4 to the target by measuring the time when the transmitted laser pulse is reflected and returned by a clock transmitter. The value measured for each predetermined angle is stored as distance measurement data with an angle from the starting point.

  Next, with reference to FIGS. 1 and 2, a bending stress / loading load measuring method according to the present invention and a bending stress / loading load measuring method by a personal computer equipped with the program will be described.

(1) Actual distance measurement (step S1)
The above-described laser distance measuring device 3 is installed inside the fixed structure (tube) 1, and the distance l _i from the laser transmitter 4 to the inner peripheral surface is measured at every angle obtained by equally dividing the entire circumference (see FIG. 3).

(2) Acquisition of data relating to the initial neutral axis (original neutral axis) (step S2)
Data 10 (see FIG. 1) relating to the initial neutral axis is in the unloaded (initial) state of the fixed structure 1 and is generally a design value of the member. Here, since the circular pipe is a target, all that is necessary is the thickness T and the elastic modulus E of the pipe material, and other data is obtained by the following calculation.

Since the separation distance from the inner peripheral surface of the pipe to the neutral axis position is 1/2 of the thickness T of the circular pipe, the value obtained by the actual distance measurement (step S1) plus this distance is the actual neutral axis position. Become. As shown in FIG. 4, when the distances l ₁ and l ₂ are obtained for the _two measuring points a1 and a2, the included angle Δψ is known, so the arc length between a1 and a2 (correctly) by the cosine theorem. Is the chord length) ΔS ₁ can be calculated. The arc length ΔS ₂ can also be calculated for the a2 and a3 measurement points by replacing a1 and a2 with a2 and a3 in the same manner as in the above procedure. Thus, ΔS _i is calculated for all the measurement points starting from the starting point. If all of this ΔS _i are added, the circumference of the tube (total neutral shaft length) is obtained.

  A member that normally resists bending has a slight change in neutral axis length compared to a change in the direction perpendicular to the neutral axis due to bending, and therefore it can be assumed that the length does not change before and after loading.

(3) Centering calculation process (step S3)
The centering calculation unit indicated by reference numeral 11 in FIG. 1 and step S3 in FIG. 2 has the following functions. That is, the positions of the vertical line 5 and the horizontal line 6 are calculated so as to accurately bisect the circumference of the circular tube (after loading) calculated from the measured neutral axis position data (after loading) (see FIG. 4). The intersection 0 of the two straight lines is used as the center of the original circular pipe (before loading), and the amount of positional deviation between this and the actual measurement reference point 4 (indicated by reference numerals 7 and 8) is examined. Based on this result, coordinate conversion 17 of the measured distance data is performed so that the distance (measured distance) and the angle of each measurement point become values measured from the center 0.

  However, when the position of the origin is changed by such coordinate conversion, there arises a problem that the angle difference between the original measurement points is not uniform. For this reason, a function is added to improve the visibility by adjusting the distance and angle data and rearranging the measurement points at positions where a certain angle difference (however, can be arbitrarily specified) is obtained. The coordinates of the neutral axis m before and after the coordinate conversion are displayed as a graph (step S4) by the graph display unit 19 in FIG. FIG. 5 shows an example of the output.

(4) Displacement calculation process (step S5)
Since the distance r (initial neutral axis position) from the center of the original circular tube is obtained, and further, the coordinate of the measured neutral axis position data is transformed so that the same point is the origin, the displacement is the difference between the two distances. As given. In general, the calculation result varies considerably due to measurement errors and errors at the time of pipe making. Therefore, the data is adjusted by the following Fourier transform process.

(5) Fourier transform process (step S6)
In the Fourier transform unit 18 (see FIG. 1), in order to be able to differentiate the measurement results according to the shape of the fixed structure, the measurement conditions, and the calculation procedure (first purpose), to average the scattered values (Second purpose) is a step of executing Fourier transform for the purpose of smoothing a change in adjacent values (third purpose). Therefore, it is used in various places in addition to step S3 in FIG.

  The Fourier transform is commonly used to average the measured values and smooth the change, but if the order of the series is increased excessively, it becomes the same as the measured values and the meaning of averaging is lost, and if the order is too low There are problems such as a large departure from reality. Therefore, it is important to set an appropriate order, but in the case of a general loading state, the displacement and bending moment can be sufficiently substituted with about the fourth order. When trying to represent the linearity of the neutral axis m, it is not necessarily uniform depending on the linearity, but it is necessary to keep the order as low as possible without departing from the original neutral axis.

  In order to check whether the order of the Fourier transform is appropriate, it is desirable to match the original data with the transformed data. A data comparison function is added to the graph display unit 19 of FIG. 1 corresponding to such a situation. The displacement graph display step S7 has the function, and it is possible to check whether the order of the series is appropriate. FIG. 6 is a display example in the displacement graph display (step S7). If it is necessary to increase or decrease the order or change it, it is programmed to change the setting easily.

  By this data comparison / contrast function, it is possible to determine whether the deformation of the neutral shaft is applied at the time of machining the member or the deformation caused by a subsequent load. For example, in the case of a round tube made of a rolled steel plate, the processing of the end of the plate is not performed correctly, so that the part welded by abutting both ends deviates from the shape of a perfect circle. Therefore, when this is observed with the data before conversion, the bent shape of the abutted portion is clearly visible while the periphery forms a smooth circle. Even if such a bent shape exists as a neutral axis, there is no displacement or bending moment unless the member is broken. This is because the displacement and bending moment change continuously (smoothly) due to the rigidity and elasticity of the member.

  Further, whether or not a member that is bent at the neutral axis m is healthy can be determined by a stress state of a portion that smoothly changes around the member. In other words, if the stress in the portion is in the elastic region, the member is originally bent, and can be considered to be sound with respect to the load. On the other hand, if the stress has reached or is close to the yield point, it is natural to think that the member has broken and bent.

  Therefore, even if the neutral axis m has a local bend, the change in displacement should be smooth unless the member is broken. When the displacement is actually expressed by a Fourier series of about the fourth order, the processing error in details is ignored and changes smoothly, and even if the data varies, it does not deviate from the vicinity of the median value. Even when the loading load increases, the result of the theory can be obtained by following the deformation of the structure correctly. In other words, by limiting the order of the series to about 4th order in the Fourier transform for displacement and bending moment, it is possible to remove the error during processing of the member and correct the deformation due to the load only by measuring the shape of the neutral shaft in the loaded state. It will be possible to calculate. This Fourier transform is shown in FIGS.

(6) Bending moment calculation process (step S8)
The bending moment is proportional to the change in curvature as shown in the above-described second equation, and the value is given by the following equation obtained by solving the equation for M.

  Here, the change in curvature is the difference in curvature before and after loading of the neutral axis m, and the specific calculation formula is (a) whether the shape of the neutral axis is a straight line or a curve, or (b) calculation of the curvature. The above-mentioned third to eighth formulas are shown depending on whether displacement or distance data is used. In the bending moment calculation section of FIG. 1, (a) a module in which the displacement of the neutral axis can be calculated is denoted by reference numeral 13, and (b) a module in which the displacement of the neutral axis is difficult and distance data is directly used is denoted by reference numeral 14. Yes. An output example (step S9) is posted in FIG.

(7) Bending stress calculation process (step S10)
If the bending moments at the respective measurement points (measurement positions) a1, a2,... Are calculated, the bending stress calculation unit 15 (see FIG. 1) and step S10 (see FIG. 2) calculate the bending stress degree from the first equation. Ask. The section modulus Z is given from the section characteristics at each measurement point. The graph display of the bending stress in step S11 is illustrated in FIG.

(8) Loading load calculation process (step S12)
This is a step of calculating the applied load by solving simultaneous equations shown in Formulas 10 to 12. This makes it possible to understand what kind of load is acting on the neutral axis of the fixed structure from the outside.

The graph display of the external load shown in step S13 is shown in FIG.
However, it is necessary to give the initial condition of this calculation depending on whether an external force acting on the shaft end or an initial value of the external load strength is assumed or actually measured.

  According to the present embodiment, based on the obtained stress (or stress distribution), it is possible to evaluate the strength of the fixed structure, or to reinforce the high stress portion as necessary. Can improve the reliability.

  Since the displacement amount, moment distribution, and bending stress at each measurement point a are displayed in a graph on the polar coordinate axis, the entire surrounding of the tube 1 can be recognized at a glance and is easy to understand.

  Using an arbitrary position in the tube 1 as a measurement reference position, the distance from the inner peripheral surface to the measurement point a is measured, and the true center position O is obtained by calculation from the measurement result. Since the actual distance and angle data are converted to those from the center position O, it is easy to perform measurement without the need for positioning.

  Next, another embodiment of the present invention will be described. In the embodiment described below, parts having the same functions and effects as those of the above-described embodiment are denoted by the same reference numerals. A detailed description of the portion is omitted, and the following description will mainly describe differences from the above-described embodiment.

  11 and 12 show a second embodiment. This second embodiment shows a retaining wall having a flat surface as an example of the fixed structure 1. In this case, as shown in FIG. 11, the laser distance measuring device (scanning laser distance measuring device) 3 is set so as to move along the reference line 0 (vertical line), and the laser transmitter 4 is set at regular intervals. The distance from the laser beam to the measurement points a1 and a2 is measured as an offset with respect to the reference line 0.

  As shown in the processing flow of FIG. 12, first, the data of the measured distance measurement with respect to the retaining wall surface is taken (step S1), and the position of the neutral axis m is determined based on the data of the cross-sectional shape of the wall (step S2). Convert to the measured neutral axis position shown. Next, after smoothing the shape of the axis using Fourier transform, the length of this axis is obtained (step S22). Since it can be assumed that the coordinate of the distance along the neutral axis obtained as the cumulative value of this length does not change with respect to the load from the side of the retaining wall, even if the axis is deformed by the loaded load, it is the same coordinate along the neutral axis. The located points point to the same place. Further, the coordinate of the neutral axis distance before the deformation can be calculated from the design of the fixed structure (step S2). The displacement is obtained by calculating how much the point at the same distance on the neutral axis has been moved by the deformation of the axis using the measured neutral axis position and design data (step S23). Since the displacement data thus obtained has a large variation due to an error, Fourier transformation is performed in step S6 so that the linearity can be smoothed and differentiated. In step S24, the curvature of the initial neutral axis is read, and in step S8, the bending moment is obtained by calculating the degree of change in curvature before and after the deformation at the same distance on the neutral axis. Further, in step S10, a bending stress degree is obtained from the obtained bending moment. The earth pressure acting on the back surface can be easily calculated by assuming that the force acting in the axial direction is the weight of the wall body (step S12).

  Here, it has been explained that the bending stress and the applied load can be measured even when the surface of the fixed structure 1 is flat by using the scanning laser distance measuring device. In addition to this, when the neutral axis of the fixed structure is curved and a rotary laser distance measuring machine is used, the neutral axis is partially fixed, or the neutral axis before and after the deformation. When the displacement can be easily calculated, for example, by measuring the linearity of from the same point, the same procedure as described here can be used.

  A third embodiment is shown in FIGS. In this third embodiment, the fixed structure 1 is a tunnel support, and it is intended to measure the stress distribution and load from A to B along the neutral axis m of this support. In this embodiment, the support 1 is a curved steel material and symmetrically arranged. However, the ceiling A is abutted on the left and right, and is structurally discontinuous at this portion. That is, this structure is a combination of members A-B having an open neutral axis m. Accordingly, it is assumed that the position of the member A-B may move due to the loading, and that no part is firmly fixed. Since it is difficult to determine the amount of displacement under such conditions, the bending moment is obtained by calculating the curvature directly from the shape of the neutral shaft and taking the difference before and after deformation.

  The measurement data acquisition (step S1), the design-related data acquisition (step S2), and the neutral axis Fourier transform (step S22) are the coordinates of the distance measured along the neutral axis and after deformation as in the second embodiment. This is the process of associating the data of the measured neutral axis position. Thereafter, displacement calculation is omitted, and the curvature of the initial neutral axis is read in step S24. In step S31, the curvature change and the bending moment are calculated from the pre-deformation curvature data in step S24 and the measured neutral axis position data Fourier-transformed in step S22 using the eighth equation. In step S32, the calculation result of the bending moment is subjected to Fourier transform again, thereby removing an error caused by expressing the neutral axis linearity by Fourier transform. Subsequent bending stress calculation (step S10) and applied load calculation (step S12) are the same as in the second embodiment.

  In the second and third embodiments, a non-periodic variable having a neutral axis opened at the time of Fourier transform is handled. The specific processing method will be described by taking the member A-B assumed in the third embodiment as an example.

  For such non-periodic variables, special care must be taken to ensure that the curvature is correctly represented to the end. Conventionally, in order to apply the Fourier transform to a non-periodic variable, the calculation is performed with an infinite period, but this method also uses the gap at the end (the difference between the coordinate axis m and the end at the end is a cap) as it is. This is because, since it is intended to be represented by a series, it is inevitable that the end portion is displaced under the condition that the order is restricted.

As shown in FIG. 14, this problem is a method in which A-B is set to A ₀ -B ₀ by rotation and translation, and this is repeated upside down and left / right inverted (same as 180 degree rotation) to create a periodic variable. It is solved with. If it can be converted into a periodic variable, the analysis method for the periodic variable may be applied as it is. However, since the length of the two sections is one period (double length), it should be noted that the order of the series is doubled. That is, the order treated as the fourth order by the periodic variable is the eighth order. That is, according to the present invention, even if there is a discontinuous portion in the fixed structure and the neutral axis m has an aperiodic shape, the stress is correctly measured over the entire fixed structure including the end. Can do.

  In this embodiment, when the applied load acting on the structure is calculated (step S12), it is desirable to know the axial force acting on the end A or B. This can be solved by measuring the load acting on the shaft end by installing a load cell at either end of either A or B for accuracy.

  If the load acting in the axial direction is large and the change in the axial length cannot be ignored, the length of the neutral axis actually measured is adjusted using the elastic modulus of the member, and the initial neutral axis It is desirable that the relationship between the distance coordinates is not shifted.

  The present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the scope of the invention.

  For example, the fixed structure may be a bridge girder or a building column or beam, and is not limited to the above-described embodiment.

It is a block diagram which shows the structure of the computer which performs the stress measuring method which concerns on 1st Embodiment. It is a flowchart which the computer which concerns on 1st Embodiment performs. It is sectional drawing which shows a measurement distance measurement process. It is a figure explaining the concept of the centering in a measurement distance measurement, and the method of displacement calculation. It is the graph which showed both the measurement distance of each measuring point, and the result of centering by the polar coordinate. It is the graph which showed the displacement amount in each measuring point, and the curve which carried out the Fourier transform of this with the polar coordinate. It is the graph which showed the curve which carried out the Fourier-transform in FIG. 6 by the orthogonal coordinate. It is the graph which showed the bending moment in each measuring point by the polar coordinate. It is the graph which showed the bending stress in each measuring point by the orthogonal coordinate. It is a graph which shows the external load in each measuring point. It is sectional drawing explaining the actual measurement distance measurement process which concerns on 2nd Embodiment. It is a flowchart which the computer which concerns on 2nd Embodiment performs. It is sectional drawing explaining the actual measurement distance measurement process which concerns on 3rd Embodiment. It is the figure explaining the concept for converting the coordinate of the neutral axis measured in 3rd Embodiment, or its displacement into a periodic variable. It is a flowchart which the computer concerning 3rd Embodiment performs.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Fixed structure 3 Laser distance measuring machine 9 Actual distance data 10 Data regarding initial neutral axis 11 Centering calculation part 12 Displacement calculation part 13 Bending moment calculation part (The curvature based on displacement and bending moment calculation)
14 Bending moment calculator (curvature and bending moment calculation based on neutral axis distance data)
DESCRIPTION OF SYMBOLS 15 Bending stress calculation part 16 Applied load calculation part 17 Coordinate transformation part 18 Fourier transformation part 19 Graph display part 20 Display part

In order to solve the above-mentioned problem, the invention described in claim 1 is directed to the surface of the fixed structure continuously from an arbitrary measurement reference position at an appropriate interval from the surface of the fixed structure on which an external force is applied. Measured distance measurement process that measures the distance to multiple measurement positions and obtains multiple continuous measured distance values, and calculates the separation distance from the surface of the fixed structure to the neutral axis position. The distance from the measurement reference position to the neutral axis of the fixed structure is added to the actual measurement distance value obtained in step 1, and these values for the adjacent measurement points and the distance from the measurement reference position or the distance of the measurement interval Based on the measured neutral axis position calculation step that calculates the length of the neutral axis using the, and the neutral axis length obtained from the measured neutral axis position calculation step, the position corresponding to the cumulative value of this length and External force acts from the magnitude of the initial curvature Displacement for determining the displacement at each measurement position of the fixed structure from the difference between the measured neutral axis position and the initial neutral axis position, and the initial neutral axis position calculation process for calculating the initial position of the neutral axis of the fixed structure By calculating the amount of change in curvature at each measurement position by differentiating the amount of displacement at each measurement position and the calculation process, the bending moment is continuously calculated by multiplying this by the elastic modulus of the fixed structure and the secondary moment of section. A bending moment calculating step for calculating, and a stress calculating step for obtaining a stress degree at an actually measured distance measurement position by dividing a moment value obtained in the bending moment calculating step by a section coefficient.

The invention described in claim 3 is characterized in that, in the invention described in claim 1 or 2, the fixed structure is a tubular body embedded in the ground.

The invention described in claim 4 is the invention described in claim 2 or 3 , wherein the fixed structure is a circular tube, and the cosine is obtained with respect to the distance and angle of each measurement point obtained in the actual distance measurement step. Using the theorem, find the circumference and shape, and calculate the center position before the fixed structure is deformed by dividing the circle of the obtained shape into two parts in the vertical and horizontal directions. And a centering step of converting the measured distance data into a distance from the center position after calculating the deviation from the measurement reference position .

According to the fifth aspect of the present invention, there is provided an arbitrary structure having an appropriate distance from the surface of the fixed structure on which an external force is applied to the fixed structure having a shape in which the axial alignment of the neutral shaft is not closed. Measuring the distance from the measurement reference position to a plurality of continuous measurement positions on the surface of the fixed structure to obtain a plurality of continuous measurement distance values, and from the surface of the fixed structure to the neutral axis position. The distance between the measurement reference position and the neutral axis of the fixed structure is calculated by adding this to the actual distance value obtained in the actual distance measurement process. Based on the measured neutral axis position calculation process that calculates the length of the neutral axis using the angle or distance value measured from the measurement reference position, and the neutral axis length obtained from the measured neutral axis position calculation process. Corresponding to the cumulative value of this length Using the initial neutral axis curvature data reading process to obtain the initial curvature data of the device and the initial curvature and actual measured neutral axis position data obtained in these processes, the change in the neutral axis curvature caused by the load is calculated. Further, by calculating the curvature and bending moment based on the neutral axis distance data from which the bending moment will be calculated, and by dividing the moment value obtained in the bending moment calculation step by the section modulus, the stress level at the measured distance measurement position And a stress calculation step for obtaining .

The invention described in claim 6 is the invention described in claim 5 , wherein the fixed structure has a linear shape, and the measurement reference position in the actual distance measuring step is arbitrary along the surface of the fixed structure. Each distance from the measurement reference line to the surface of the fixed structure is measured by a scanning laser distance measuring device that travels on a rail installed on the measurement reference line .

The invention described in claim 7 is the invention described in any one of claims 1 to 6 , wherein the measured distance or the displacement amount is Fourier-transformed in the measured neutral axis position calculating step and the displacement calculating step. These values are averaged and the change is made into a smooth curve, followed by differentiation .

In the invention described in claim 8, in the invention described in claim 7, when the fixed structure has an end portion without forming a ring, an actually measured distance or displacement from the end portion to an arbitrary position. It is characterized in that a virtual curve that is continuous at the end and changes periodically every double length is drawn and differentiated by connecting the inverted curve of the quantity on the graph at the end. .

The invention described in claim 9 is the invention described in any one of claims 1 to 8, wherein the balance between force and moment is applied to a minute portion on the neutral axis of the fixed structure after the stress calculation step. An external load acting on the axis of the neutral axis by establishing simultaneous equations from the relationship and starting the intersection with the axis end where the initial conditions can be set or the symmetry axis and solving the simultaneous equations sequentially along the neutral axis An external load calculating step for obtaining the above is provided.

The invention described in claim 10 is a program for causing a computer to perform the process according to any one of claims 1 to 9. The invention described in claim 11 is a computer that executes the program described in claim 10 .

In claim 5 , the method of obtaining the curvature directly from the measured distance measurement result is as follows.

As is apparent from the above equation, the curvature is obtained by differentiating the length (distance). However, since the actual measurement value includes an error, a correct solution cannot be obtained by differentiating it as it is. Therefore, this problem is solved by applying the Fourier transform in claim 7 to average the measured values and smooth the change. In other words, the following equation is used to convert displacement or distance equal length data into a Fourier-class mathematical expression, so that not only the average value of the data but also the differential coefficient obtained when it is differentiated can be obtained. It is a thing.

In the eighth aspect of the invention, the method for enabling the Fourier transform to be applied to a non-periodic variable is specifically as follows. In this case, the variable can be either Li = f (φi) shown in polar coordinates or Yi = f (xi) shown in Cartesian coordinates (see FIG. 14).

The external load calculation step of claim 9 is based on the following formula.
Taking a minute section on the neutral axis of the fixed structure, assuming the end point as 1 and the end point as 2, and assuming the end face perpendicular to the neutral axis at those points, the direction of each surface and the force generated on each surface And moment (internal force) are expressed as follows.

Since the distance measurement is for knowing the displacement of the neutral axis of the fixed structure or the shape thereof, the installation position of the distance measuring device can be arbitrarily determined if this purpose can be achieved. In particular, in the case of a fixed structure with a neutral shaft closed, the original center position can be obtained by the centering method according to claim 4 , so that the displacement can be easily calculated.

In order to solve the above-mentioned problem, the invention described in claim 1 is directed to the surface of the fixed structure continuously from an arbitrary measurement reference position at an appropriate interval from the surface of the fixed structure on which an external force is applied. Measured distance measurement process that measures the distance to multiple measurement positions and obtains multiple continuous measured distance values, and calculates the separation distance from the surface of the fixed structure to the neutral axis position. The distance from the measurement reference position to the neutral axis of the fixed structure is added to the actual measurement distance value obtained in step 1, and these values for the adjacent measurement points and the distance from the measurement reference position or the distance of the measurement interval Based on the measured neutral axis position calculation step that calculates the length of the neutral axis using the, and the neutral axis length obtained from the measured neutral axis position calculation step, before the deformation corresponding to the position on the neutral axis from the size of the initial curvature at position From the initial neutral axis position calculation step of calculating the initial position of the neutral axis of the fixed structure in a state where no force is applied, and the difference between the measured neutral axis position and the initial neutral axis position, Displacement calculation process to obtain the displacement amount, the displacement amount at each measurement position is differentiated to obtain the amount of change in curvature at each measurement position, and this is continuously multiplied by the elastic modulus of the fixed structure and the cross-sectional second moment. A bending moment calculating step for calculating a bending moment and a stress calculating step for obtaining a stress degree at an actually measured distance measurement position by dividing a moment value obtained in the bending moment calculating step by a section modulus. And

The invention described in claim 4 is obtained in the actual distance measurement step before the displacement calculation in the displacement calculation step when the fixed structure is a circular pipe in the invention described in claim 2 or 3. Obtain the circumference and shape using the cosine theorem for the distance and angle of each measured point, and divide the circle of the obtained shape into two parts in the vertical and horizontal directions before the fixed structure is deformed calculating the center position, after calculating the deviation between the measurement reference position at the central position and the distance measuring comprises a centering step of converting the measured distance data to the distance from the center position, it converted to a distance from said central position It characterized that you calculate the displacement amount in the displacement calculating step using measured distance data.

According to the fifth aspect of the present invention, there is provided an arbitrary structure having an appropriate distance from the surface of the fixed structure on which an external force is applied to the fixed structure having a shape in which the axial alignment of the neutral shaft is not closed. Measuring the distance from the measurement reference position to a plurality of continuous measurement positions on the surface of the fixed structure to obtain a plurality of continuous measurement distance values, and from the surface of the fixed structure to the neutral axis position. The distance between the measurement reference position and the neutral axis of the fixed structure is calculated by adding this to the actual distance value obtained in the actual distance measurement process. Based on the measured neutral axis position calculation process that calculates the length of the neutral axis using the angle or distance value measured from the measurement reference position, and the neutral axis length obtained from the measured neutral axis position calculation process. Te, change corresponding to the position on the neutral axis The curvature data reading step of an initial neutral axis to obtain the initial curvature data in the previous position, using the data of the measured neutral axis position and the initial curvature obtained in these steps, the change in curvature of the neutral axis caused by the mounting load By further calculating the curvature and bending moment based on the neutral axis distance data from which the bending moment is calculated, and dividing the moment value obtained in the bending moment calculation step by the section modulus, And a stress calculation step for obtaining a stress level.

Claims (10)

By measuring the distance from any measurement reference position that is appropriately spaced from the surface of the fixed structure on which an external force is acting to multiple consecutive measurement positions on the surface of the fixed structure, multiple actual measurements An actual distance measurement step for obtaining a distance value;
By calculating the separation distance from the surface of the fixed structure to the neutral axis position and adding this to the actual distance value obtained in the actual distance measurement process, the distance from the measurement reference position to the neutral axis of the fixed structure is obtained. An actual neutral axis position calculation step of calculating the length of the neutral axis using these values for adjacent measurement points and the distance value of the angle or measurement interval viewed from the measurement reference position;
Based on the length of the neutral axis obtained from the measured neutral axis position calculation process, the fixed structure in the state where no external force is applied from the position corresponding to the cumulative value of this length and the magnitude of the initial curvature An initial neutral axis position calculating step for calculating the initial position of the vertical axis;
A displacement calculating step for obtaining a displacement amount at each measurement position of the fixed structure from a difference between the measured neutral axis position and the initial neutral axis position;
Bending moment that continuously calculates the bending moment by differentiating the displacement at each measuring position to obtain the amount of change in curvature at each measuring position and multiplying this by the elastic modulus of the fixed structure and the secondary moment of section A calculation process;
By dividing the moment value obtained in the bending moment calculation step by the section modulus, a stress calculation step for obtaining the degree of stress at the measured distance measurement position;
In a small part on the neutral axis of a fixed structure, a simultaneous equation is established from the relationship between the balance of force and moment, and the initial condition is set as the starting point of the intersection with the axis end or the axis of symmetry, and then along the neutral axis. And an external load calculating step of obtaining an external load acting on the axis of the neutral axis by solving simultaneous equations in a fixed manner.   The fixed structure has an arc shape, and the actual distance measuring step is performed by measuring a distance from the measurement reference position to the surface of the fixed structure by a rotary laser distance measuring device installed at a measurement reference position inside the fixed structure. The method for measuring a bending stress of a fixed structure according to claim 1, wherein the measurement is performed at continuous angles.   3. The method for measuring the bending stress of a fixed structure according to claim 2, wherein the fixed structure is a tube embedded in the ground.   The fixed structure has a linear shape, and the measurement reference position in the actual distance measurement step is a measurement reference line that is an arbitrary straight line along the surface of the fixed structure, and runs on a rail installed on the measurement reference line. The method for measuring a bending stress of a fixed structure according to claim 1, wherein each distance from the measurement reference line to the surface of the fixed structure is measured by a scanning laser distance measuring machine.   2. The measured neutral axis position calculating step and the displacement calculating step, wherein the measured distance or the amount of displacement is Fourier-transformed, these values are averaged, and the change is converted into a smooth curve, and then differentiated. 2. A bending stress measurement method for a fixed structure according to 1.   When the fixed structure has an end without forming a ring, by connecting the measured distance from the end to the arbitrary position or the change curve of the amount of displacement on the graph at the end 2. The bending stress measuring method for a fixed structure according to claim 1, wherein the bending stress is differentiated by drawing an imaginary curve which is continuous at the end portion and periodically changes every double length.   The fixed structure is a circular pipe, and the perimeter and shape are determined using the cosine theorem for the distance and angle of each measurement point obtained in the actual distance measurement process. Calculate the center position before the fixed structure is deformed by dividing it into two directions, calculate the deviation between this center position and the measurement reference position during distance measurement, and then change the measured distance data to the distance from the center position. The method for measuring a bending stress of a fixed structure according to claim 2, further comprising a centering step for conversion. For a fixed structure in which the neutral axis of the neutral axis has an arbitrary shape, from any measurement reference position at an appropriate distance from the surface of the fixed structure on which an external force is acting, An actual distance measurement step of measuring a distance to a plurality of consecutive measurement positions and obtaining a plurality of continuous actual distance values;
By calculating the separation distance from the surface of the fixed structure to the neutral axis position and adding this to the actual distance value obtained in the actual distance measurement process, the distance from the measurement reference position to the neutral axis of the fixed structure is obtained. An actual neutral axis position calculation step of calculating the length of the neutral axis using these values for adjacent measurement points and the distance value of the angle or measurement interval viewed from the measurement reference position;
Based on the length of the neutral axis obtained from the measured neutral axis position calculation step, the initial neutral axis curvature data reading step for acquiring the initial curvature data of the position corresponding to the cumulative value of this length;
Using the initial curvature data obtained in these steps and the measured neutral axis position data, the change in the neutral axis curvature caused by the loading load is calculated, and the curvature based on the neutral axis distance data from which the bending moment is calculated. Bending moment calculation process,
By dividing the moment value obtained in the bending moment calculation step by the section modulus, a stress calculation step for obtaining the degree of stress at the measured distance measurement position;
In a small part on the neutral axis of a fixed structure, a simultaneous equation is established from the relationship between the balance of force and moment, and the initial condition is set as the starting point of the intersection with the axis end or the axis of symmetry, and then along the neutral axis. And an external load calculating step of obtaining an external load acting on the axis of the neutral axis by solving simultaneous equations in a fixed manner.   The recording medium which recorded the program which performs the process of any one of Claims 1-8. A computer that executes the program according to claim 9.

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