JP2013092463A - Measurement system for build-in error of steel pipe, measurement method for build-in error of steel pipe, and building-in method for inverted construction column - Google Patents

Abstract

PROBLEM TO BE SOLVED: To facilitate an installation operation for a device used to measure a build-in error of a steel pipe, and to measure the build-in error while correcting a build-in attitude of the steel pipe.SOLUTION: There is provided a system 100 which measures a build-in error of an inverted construction column built in a foundation on the basis of a position of a target 50 provided in the inverted construction column 10. The system includes a camera 110 installed in the head of the inverted construction column 10 so as to photograph the target 50, an inclinometer 120 installed in the head of the inverted construction column 10, and a computer 130 which extracts the position of the target 50 on the basis of imaging information of the camera 110, calculates an angle of inclination of an optical axis 112 of the camera 110 to a perpendicular axis on the basis of a measured value of the inclinometer 120, and corrects the position of the target 50 on the basis of the calculated angle of inclination.

Description

  The present invention relates to a measurement system, a measurement method, and a reverse strut erection method for measuring an erection error of a steel pipe erected on the ground.

  When constructing an underground structure of a building by the reverse driving method, a steel pipe is embedded in the ground as a reverse strut to support the load of the building's frame before excavating the ground. When this steel pipe is inclined, it has a great influence on the connection with the beam and the construction of the ground steel frame. Therefore, it is important to ensure vertical accuracy when embedding the steel pipe.

  For this reason, the installation of a steel pipe as a reverse strut is carried out while measuring the error.For example, a mark is given to a plate provided inside the steel pipe, a laser vertical device is installed on the head of the steel pipe, The steel pipe erection error is measured based on the positional relationship between the laser beam and the laser beam (see, for example, Patent Document 1).

JP 2011-117803 A

  However, in the measurement method described in Patent Document 1, it is necessary to install the laser vertical device horizontally (so that the optical axis of the laser is vertical) with high accuracy, and high-level work is required. In addition, when the erection posture of the back strut is corrected, the horizontality of the laser vertical tool is lost, so that the erection error cannot be measured while correcting the erection posture of the counter strut.

  The present invention has been made in view of the above problems, and facilitates the installation work of the apparatus used for measuring the steel pipe erection error and measures the erection error while correcting the erection posture of the steel pipe. It is an object to make it possible.

  The steel pipe erection error measuring system according to the present invention is a system for measuring the erection error of a steel pipe installed in the ground based on the position of an index provided inside the steel pipe, A camera installed on the head of the camera so as to photograph the index, an inclinometer installed on the head of the steel pipe, and an index position extraction unit that extracts the position of the index based on imaging information of the camera And an inclination angle of the optical axis of the camera with respect to the vertical axis based on the measured value of the inclinometer, and the position of the index extracted by the index position extraction unit is corrected based on the calculated inclination angle. An index position correction unit.

  In the steel pipe erection error measurement system, the index position correction unit calculates the inclination angle corresponding to the measurement value of the inclinometer from a relational expression indicating the relationship between the measurement value of the inclinometer and the inclination angle. It may be calculated.

  Further, the method for measuring the error of erection of the steel pipe according to the present invention is a method of measuring the erection error of the steel pipe erected on the ground based on the position of the index provided inside the steel pipe, A step of installing a camera and an inclinometer on the head of a steel pipe and photographing the index with the camera, a step of extracting a position of the index based on imaging information of the camera, and a measurement value of the inclinometer And calculating the tilt angle of the optical axis of the camera with respect to the vertical axis, and correcting the position of the extracted index based on the calculated tilt angle.

  In the method of measuring the steel pipe erection error, in the step of calculating the inclination angle, the inclination corresponding to the measurement value of the inclinometer is obtained from a relational expression indicating the relationship between the measurement value of the inclinometer and the inclination angle. An angle may be calculated.

  The steel pipe erection error measuring method may include a step for obtaining the relational expression. In this step, a camera and the inclinometer are installed on the head of the steel pipe, and the index is obtained by the camera. A first step of photographing and extracting the position coordinates of the index based on imaging information of the camera; and rotating the camera and the inclinometer around the vertical axis by 180 ° about the camera, and A second step of photographing the index and extracting the position coordinates of the index based on imaging information of the camera, and calculating an average value of the position coordinates of the index extracted in the first step and the second step The third step and the fourth step of calculating the tilt angle in the first step based on the average value calculated in the third step are performed a plurality of times to perform the tilt You may be obtained in measurements with linear equations with the inclination angle.

  Further, the method of erection of the backlash strut according to the present invention is a method of erection of the backlash strut on the ground, wherein the backlash strut is provided with a camera and an inclinometer on the head and provided with an index inside. Erected on the ground, photographing the index with the camera, extracting the position of the index based on imaging information of the camera, and vertical of the optical axis of the camera based on the measured value of the inclinometer A step of calculating an inclination angle with respect to an axis, a step of correcting the position of the extracted index based on the calculated inclination angle, and an error in erection of the striking strut based on the corrected position of the index A step of calculating, and a step of correcting the erection posture of the striking strut so as to reduce the calculated erection error.

  ADVANTAGE OF THE INVENTION According to this invention, while installing the apparatus used for the measurement of the erection error of a steel pipe becomes easy, the erection error can be measured while correcting the erection posture of the steel pipe.

It is a figure which shows the striking strut built in the ground. It is a figure which shows the outline of the measurement system of an erection error. It is a block diagram which shows schematic structure of a computer. It is a figure which shows the relationship between inclination-angle ((beta) x, (beta) y), a position coordinate (Xt, Yt), and a position coordinate (Xr, Yr). It is a graph which shows the relationship between the measurement data ((alpha) x, (alpha) y) of an inclinometer, and the inclination angle ((beta) x, (beta) y) of a camera. It is a flowchart which shows the procedure which calculates | requires following (1) Formula. It is a figure for demonstrating the procedure which calculates | requires the following (1) Formula. It is a flowchart which shows the procedure which measures the erection error (Xr, Yr) of the reverse strut. It is a flowchart for demonstrating the calculation process of the position coordinate (Xr, Tr) by a computer. (A)-(E) is a figure which shows the operation | work procedure which builds a back strut strut. It is a figure which shows the operation | work procedure which installs a reverse strut. It is a flowchart for demonstrating the procedure which corrects the erection attitude | position of the back strut 10.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings. FIG. 1 is a view showing a backlash strut 10 built in the ground. As shown in this figure, the counter strut 10 includes an upper column portion 20 and a lower pile portion 30, and a base plate 40 is interposed between the column portion 20 and the pile portion 30.

  The pile portion 30 is made of a so-called cross H-shaped steel 31 and a stud 32 is provided on the outer surface near the lower end portion of the flange 31A. This pile portion 30 is embedded in a pile 1 made of reinforced concrete. The column portion 20 is made of a steel pipe 21 having a rectangular cross section, and a diaphragm 22 is attached to a height position where the beams on each floor inside the steel pipe 21 are to be connected. The diaphragm 22 attached to the steel pipe 21 is formed with a circular hole 22A. When constructing a ground frame, the steel pipe 21 is filled with concrete through the hole 22A to form a CFT column. .

  Further, on the upper surface of the base plate 40, a plate-like target 50 used for measuring the erection error of the back strut 10 is attached. A circular reflecting mirror 51 is affixed to the upper surface of the target 50, and the target 50 has a position where the center of the reflecting mirror 51 passes through the core of the counter-strut 10 (a position where the central axis of the steel pipe 21 passes). ) To match.

  FIG. 2 is a diagram showing an outline of the erection error measurement system 100. As shown in this figure, the erection error measurement system 100 includes a measurement unit 101 installed on the head of the back strut 10 and a computer 130. The measurement unit 101 includes a plate 102 and a camera 110 and an inclinometer 120 installed thereon. The computer 130 is connected to the camera 110 and the inclinometer 120 in a wired or wireless manner, and receives imaging data of the camera 110 and measurement data of the inclinometer 120. Further, the computer 130 is installed with a program for executing a process of calculating the erection error of the back strut 10 based on the image data of the camera 110 and the measurement value of the inclinometer 120.

  A Yatco 104 is installed on the head of the back strut 10, a reference line is written on the upper surface of the Yatco 104, and the plate 102 is installed on the upper surface of the Yatco 104 according to the reference line. An opening through which the core of the counter strut 10 passes is formed on the upper surface of the plate 102 and the YATCO 104, and the camera 110 is installed downward so that the optical axis 112 passes through the opening. That is, the camera 110 is installed so as to photograph the reflecting mirror 51 of the target 50.

  The inclinometer 120 is a strain gauge type inclinometer that is usually used to measure the inclination of the ground, and the inclination angle αx in two directions (X direction and Y direction) orthogonal to the horizontal plane of the installation surface (plate 102). , Αy is measured.

  FIG. 3 is a block diagram illustrating a schematic configuration of the computer 130. As shown in this figure, the computer 130 includes a CPU 132, a memory 134, an interface 136, and a monitor 138. The CPU 132 includes a position coordinate extraction unit 132A and a position coordinate correction unit 132B. The interface 136 inputs imaging data output from the camera 110 and measurement data (αx, αy) output from the inclinometer 120. The memory 134 stores a program for extracting a position coordinate (Xt, Yt) of the center point of the reflecting mirror 51 and correcting the value, and the CPU 132 performs processing according to the program. And the calculated value is displayed on the monitor 138.

  The position coordinate extraction unit 132A extracts the position coordinates (Xt, Yt) of the center point of the reflecting mirror 51 based on the imaging data input by the interface 136. The origin of this coordinate system is the intersection of the height surface of the reflecting mirror 51 and the optical axis 112. Then, the position coordinate correction unit 132B corrects the position coordinates (Xt, Tt) based on the measurement data (αx, αy) of the inclinometer 120 so that the actual (that is, the camera 110 is accurately horizontal (optical axis 112)). Position coordinates (Xr, Yr) are calculated.

Here, the position coordinate correction unit 132 </ b> B is based on the relational expression (equation (1) below) between the measurement data (αx, αy) of the inclinometer 120 and the inclination angle (βx, βy) of the camera 110. The inclination angle (βx, βy) is calculated, and based on the relational expression (the following expression (2)) between the inclination angle (βx, βy), the position coordinate (Xt, Yt), and the position coordinate (Xr, Yr) Coordinates (Xr, Yr) are calculated. Note that ax, bx, ay, by, and L will be described later.
(Βx, βy) = (ax · αx + bx, ay · αy + by) (1)
(Xr, Yr) = (Xt + Lsin βx, Yt + Lsin βy) (2)

  Hereinafter, the relationship between the measurement data (αx, αy) of the inclinometer 120 and the tilt angle (βx, βy) of the camera 110, the tilt angle (βx, βy), the position coordinate (Xt, Yt), and the position coordinate (Xr) , Yr).

  FIG. 4 is a diagram illustrating a relationship among the tilt angle (βx, βy), the position coordinates (Xt, Yt), and the position coordinates (Xr, Yr). Although FIG. 4 shows only the X direction, the same applies to the Y direction. As shown on the left side of FIG. 4, when the tilt angle (βx, βy) of the camera 110 is (0, 0), the core 12 and the optical axis as when the striking strut 10 is correctly erected. 112 matches, the actual position coordinates (Xr, Yr) of the target 50 and the position coordinates (Xt, Yt) in the captured image 114 of the camera 110 match.

  On the other hand, when the camera 110 is tilted and the distance from the camera 110 to the target 50 is L as shown on the right side of FIG. 4, the actual position coordinates (Xr, Yr) of the target 50 and the photographing of the camera 110 are taken. The position coordinates (Xt, Yt) in the image 114 deviate, and the relationship of the above expression (2) is obtained.

  FIG. 5 is a graph showing the relationship between the measurement data (αx, αy) of the inclinometer 120 and the inclination angle (βx, βy) of the camera 110. This graph shows only αx and βx values in the X direction, but the same applies to αy and βy values in the Y direction. As shown in this graph, the measurement capacity of the inclinometer 120 is ± α ′ ° (for example, ± 1 to 5 °), and in that range, the resistance change amount of the strain gauge of the inclinometer 120 and the measured values (αx, αy). ), The linearity as shown in the above equation (1) is also established in the measurement data (αx, αy) of the inclinometer 120 and the inclination angle (βx, βy) of the camera 110. can do.

  FIG. 6 is a flowchart showing a procedure for obtaining the equation (1), and FIG. 7 is a diagram for explaining a procedure for obtaining the equation (1). First, as shown on the left side of FIG. 7, the measurement unit 101 is installed on the upper surface of the YATCO 104 in accordance with the reference line (step 1). The position where the measurement unit 101 is installed in this step is the installation position when measuring the erection error. Next, the target 110 is imaged with the camera 110 (step 2). In this step, the position coordinate extraction unit 132A extracts the position coordinates (Xt1, Yt1).

  Next, as shown on the right side of FIG. 7, the measurement unit 101 is rotated about the vertical axis about the optical axis 112 of the camera 110 by 180 ° and installed on the YATCO 104 according to the reference line (step 3). Next, the target 110 is imaged with the camera 110 (step 4). In this step, the position coordinate extraction unit 132A extracts the position coordinates (Xt2, Yt2).

Next, actual position coordinates (Xr, Yr) are calculated from the following equation (3) (step 5). Here, when the tilt angle of the camera 110 in steps 1 and 2 is (βx1, βy1), the tilt angle of the camera 110 in steps 3 and 4 is (−βx1, −βy1), and extracted in step 2. By calculating the average value of the position coordinates (Xt1, Yt1) and the position coordinates (Xt2, Yt2) extracted in step 4, the actual position coordinates (Xr, Yr) can be obtained.
(Xr, Yr) = ((Xt1-Xt2) / 2, (Yt1-Yt2) / 2) (3)

  Next, the tilt angle (βx1, βy1) of the camera 110 is calculated by substituting the position coordinates (Xr, Yr) calculated in step 5 into the equation (2) (step 6).

  Then, by performing Steps 1 to 6 again, the inclination angle (βx2, βy2) when the second measurement unit 101 is installed is obtained (Step 7).

Here, when the tilt angle (βx, βy) of the camera 110 is (βx1, βy1), the measurement data of the inclinometer 120 is (αx1, αx1), and the tilt angle (βx, βy) of the camera 110 is (βx2). , Βy2), the measurement data of the inclinometer 120 is assumed to be (αx2, αx2), and ax, bx, ay, and by the above equation (1) are calculated (step 8).
ax = (βx1-βx2) / (αx1-αx2)
bx = (αx1, βx2-αx2, βx1) / (αx1-αx2)
ay = (βy1-βy2) / (αy1-αy2)
by = (αy1 · βy2-αy2 · βy1) / (αy1-αy2)

  A program including a relational expression (the above expression (1)) between the tilt angle (βx, βy) of the camera 110 and the measured value (αx, αy) of the inclinometer 120 obtained as described above is stored in the memory 134. The CPU 132 calculates actual position coordinates (Xr, Yr) according to the program.

  FIG. 8 is a flowchart showing a procedure for measuring the erection error (Xr, Yr) of the back strut 10. As shown in this flowchart, first, the distance L between the camera 110 and the target 50 is input to the computer 130 (step 11). Next, the measurement unit 101 is installed on the YATCO 104 in accordance with the reference line (step 12). Next, the target 110 is imaged with the camera 110 (step 13).

  FIG. 9 is a flowchart for explaining the calculation process of the position coordinates (Xr, Tr) by the computer 130. As shown in this flowchart, when the target 50 is imaged by the camera 110, the position coordinate extraction unit 132A extracts the position coordinates (Xt, Yt) from the imaging data (step 131). Then, the position coordinate correcting unit 132B calculates the tilt angle (βx, βy) of the camera 110 from the measured values (αx, αy) of the inclinometer 120 by the above formula (1), and the position coordinates (Xt, Yt), tilt Based on the angle (βx, βy) and the distance L between the camera 110 and the target 50, the position coordinates (Xr, Yr) are calculated by the above equation (2) (step 132).

  As described above, the measurement error of the position coordinates (Xt, Yt) of the target 50 due to the tilt of the optical axis 112 of the camera 110 with respect to the vertical axis can be corrected, and the installation of the camera 110 on the back strut 10 is performed. Regardless of the state, the erection error (Xr, Yr) of the striking strut 10 can be accurately measured. Therefore, the installation work of the camera 110 is easy.

  In addition, even if the installation state of the camera 110 installed on the head is corrected by correcting the erection of the back strut 10, accurate measurement in the changed state is performed without correcting the installation state of the camera 110. Therefore, the erection error (Xr, Yr) can be measured while correcting the erection posture of the back strut 10.

  10 (A) to 10 (E) and FIG. 11 are diagrams showing a work procedure for installing the back strut 10. First, as shown in FIG. 10A, a hole 2 for constructing the pile 1 is excavated by a known excavator such as an earth drill excavator, and necessary operations such as bottom preparation and slime treatment are performed. . Moreover, the casing 3 is built in a surface layer part. Next, as shown in FIG. 10B, the gantry 6 for supporting the counter-strut 10 is installed on the ground so as to straddle the hole 2. Then, the reinforcing bar 5 is built in the hole 2 by hanging the reinforcing bar 5 with the crane 4 and lowering it to the bottom of the hole 2.

  Next, as shown in FIG. 10 (C), a Yatsuko 104 is attached to the head of the counter strut 10 and the measurement unit 101 is installed on the upper part thereof in accordance with the reference line. Then, the back strut 10 is erected and then built into the hole 1. Further, a water pipe 13 for supplying the stabilizing liquid is built in the hole 1.

  Next, as shown in FIG. 11, the height of the head of the striking strut 10 and the position in the horizontal direction are adjusted. Thereafter, by adjusting the horizontal position of the lower portion of the striking strut 10, the verticality (building posture) of the core of the striking strut 10 is adjusted.

  A plurality of journal jacks 7 are installed on the gantry 6, and the backlash struts 10 are supported by the plurality of journal jacks 7 through the yatco 104. The journal jack 7 is a screw-type jack that expands and contracts in the vertical direction, and the height of the head of the counter strut 10 can be adjusted by expanding and contracting the journal jack 7.

  Further, a plurality of (for example, four as shown) pantograph jacks 8 and guide tubes 9 are installed between the casing 3 and the counter strut 10. A counter strut 10 is inserted into the guide tube 9, and a plurality of pantograph jacks 8 are arranged around the guide tube 9 at predetermined intervals. The plurality of pantograph jacks 8 are pantograph type hydraulic jacks, which take a reaction force on the casing 3 and press the guide tube 9 toward the center of the hole 2. By extending or contracting the plurality of pantograph jacks 8 in the radial direction of the hole 2, the horizontal position of the lower portion of the counter strut 10 can be adjusted.

  Next, as shown in FIG. 10 (D), the tremy tube 11 is built in the hole 2 and concrete is placed below the hole 2. At this time, by adjusting the position in the horizontal direction of the lower portion of the striking strut 10, the erection posture of the striking strut 10 is adjusted.

  Then, after removing the tremy tube 11, the concrete is cured, and the gantry 6 and the Yatco 104 are removed in a state where the back strut 10 is temporarily fixed. Thereafter, as shown in FIG. 10 (E), the back strut 10 is buried in the ground by backfilling the soil with the top of the hole 2.

  FIG. 12 is a flowchart for explaining a procedure for correcting the erection posture of the back strut 10. As shown in this flowchart, first, the distance L between the camera 110 and the target 50 is input to the computer 130 (step 101). Here, the measuring unit 101 is installed on the YATCO 104 in accordance with the reference line before installing the back strut 10.

  Next, the target 50 is photographed with the camera 110 (step 102). As described above, when the target 50 is photographed by the camera 110, the position coordinate extraction unit 132A extracts the position coordinate (Xt, Yt), and the position coordinate correction unit 132B detects the measured value (αx of the inclinometer 120). , Αy) to calculate the tilt angle (βx, βy) of the camera 110 and correct the position coordinate (Xt, Yt) based on the tilt angle (βx, βy) to calculate the position coordinate (Xr, Yr). .

  Next, it is determined whether or not the erection error (Xr, Yr) measured by the erection error measurement system 100 is within the management value (step 103). 8 corrects the erection posture of the back strut 10 (step 104). At this time, until the erection error (Xr, Yr) measured by the erection error measuring system 100 falls within the control value, the correction of the erection posture of the back strut 10 by the pantograph jack 8 is continued.

  As described above, after the camera 110 is installed on the head of the back strut 10, regardless of the installation state of the camera 110 on the back strut 10, the installation error ( Xr, Yr) can be measured accurately. Therefore, not only before placing the concrete of the pile 1 after placing the reverse strut 10 but also during the concrete placement of the pile 1 thereafter (Xr, Yr) It is possible to correct the erection posture of the striking strut 10 while measuring.

  In addition, in the said embodiment, although the pile part 30 was comprised with the cross H-shaped steel 31, not only this but appropriate steel materials, such as H-shaped steel and a square steel pipe, can be used. Moreover, in the said embodiment, although the column part 20 was comprised with the square steel pipe 21, it is not restricted to this, A round steel pipe can also be used.

  Moreover, in the said embodiment, although the case where the installation error of the back strut 10 built in the ground was measured was demonstrated, not only this but if it is a case where the steel pipe to which the base plate 40 was connected to the lower end is built. The present invention can be applied. In addition, the base plate 40 is not necessarily provided, and the present invention can be applied if the plate is attached so as to close the inside of the steel pipe.

1 pile, 2 holes, 3 casing, 4 crane, 5 reinforcing bar, 6 mount, 7 journal jack, 8 pantograph jack, 9 guide pipe, 10 counter strut (steel pipe), 11 tremy pipe, 12 cores, 13 water pipe, 20 pillars, 21 steel pipes, 22 diaphragms, 22A holes, 30 piles, 31 H-shaped steel, 31A flanges, 32 studs, 40 base plates, 50 targets, 51 reflectors, 100 installation error measurement systems, 101 measurement units, 102 Plate, 104 Yatco, 110 Camera, 112 Optical axis, 114 Photographed image, 120 Inclinometer, 130 Computer, 132 CPU, 132A Position coordinate extraction unit, 132B Position coordinate correction unit, 134 Memory, 136 interface, 138 monitor

Claims (6)

A system for measuring an erection error of a steel pipe erected on the ground based on a position of an index provided inside the steel pipe,
A camera installed on the head of the steel pipe so as to photograph the index;
An inclinometer installed at the head of the steel pipe;
An index position extraction unit that extracts a position of the index based on imaging information of the camera;
An index position for calculating an inclination angle of the optical axis of the camera with respect to a vertical axis based on a measurement value of the inclinometer, and correcting the position of the index extracted by the index position extraction unit based on the calculated inclination angle A correction unit;
An error measurement system for steel pipes equipped with   2. The steel pipe construction according to claim 1, wherein the index position correction unit calculates the inclination angle corresponding to the measurement value of the inclinometer from a relational expression indicating a relationship between the measurement value of the inclinometer and the inclination angle. Insertion error measurement system. A method of measuring an erection error of a steel pipe erected on the ground based on a position of an index provided inside the steel pipe,
Installing a camera and an inclinometer on the head of the steel pipe and photographing the index with the camera;
Extracting the position of the index based on imaging information of the camera;
Calculating an inclination angle of the optical axis of the camera with respect to a vertical axis based on a measurement value of the inclinometer;
Correcting the position of the extracted index based on the calculated tilt angle;
Method for measuring the erection error of a steel pipe comprising   The steel pipe according to claim 3, wherein in the step of calculating the inclination angle, the inclination angle corresponding to the measurement value of the inclinometer is calculated from a relational expression indicating a relationship between the measurement value of the inclinometer and the inclination angle. Of measuring the erection error. A step for obtaining the relational expression;
In this step,
A first step of installing the camera and the inclinometer on the head of the steel pipe, photographing the index with the camera, and extracting position coordinates of the index based on imaging information of the camera;
A second step of rotating the camera and the inclinometer by 180 ° about the vertical axis about the camera, photographing the index with the camera, and extracting position coordinates of the index based on imaging information of the camera; When,
A third step of calculating an average value of the position coordinates of the index extracted in the first step and the second step;
A fourth step of calculating the tilt angle in the first step based on the average value calculated in the third step;
5. The method of measuring a steel pipe erection error according to claim 4, wherein a linear equation between the measured value of the inclinometer and the inclination angle is obtained by performing a plurality of times. It is a method of laying back struts on the ground,
Installing a camera and an inclinometer on the head, erected the striking strut with an index inside, and shooting the index with the camera;
Extracting the position of the index based on imaging information of the camera;
Calculating an inclination angle of the optical axis of the camera with respect to a vertical axis based on a measurement value of the inclinometer;
Correcting the position of the extracted index based on the calculated tilt angle;
Based on the corrected position of the indicator, calculating a erection error of the backlash strut,
Correcting the erection posture of the striking strut so as to reduce the calculated erection error;
A method of erection of a striking strut with

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