A testing device and method for arch ring deflection of arch bridges based on beam strain and inclination angle.

Abstract

This invention discloses a testing device and method for testing the deflection of an arch bridge arch ring based on the strain and inclination angle of a small beam. The testing device consists of a simulated beam positioned parallel to the arch ring of the arch bridge under test. This simulated beam is composed of multiple small beam segments and is connected to the arch bridge via a rigid support device. The rigid support device transmits the deflection. By installing inclination sensors on the small beams and strain gauges at the locations of deflection measurement points, the corresponding strain and inclination angle values ​​can be measured. The deflection curve of the small beams can then be calculated using the testing method provided by this invention, thereby determining the deflection at the measurement points on the arch ring of the arch bridge under test. This device and corresponding testing method offer high accuracy while simplifying operation, significantly improving testing efficiency.

Description

Technical Field

[0001] This invention relates to the field of bridge inspection technology, and in particular to a test device and method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the beam. Background Technology

[0002] Bridge deflection is a crucial parameter for bridge structures, directly reflecting their overall vertical stiffness and serving as a vital indicator of linear changes in the bridge's structure. The deflection of the arch ring of an arch bridge is closely related to its load-bearing capacity and its ability to withstand dynamic loads such as earthquakes. Testing the arch ring deflection is not only significant for assessing the load-bearing capacity and earthquake preparedness, but also for accumulating valuable experience in improving arch bridge theory and construction. Therefore, accurate testing of arch bridge deflection is essential. Previously, deflection testing often involved installing instruments on actual bridges, but installing and dismantling instruments on the arch ring of an arch bridge is extremely difficult. For example, Chinese invention patent application number 201410160000.8 provides a method and apparatus for accurately measuring the deflection of the main arch rib of a cable-stayed (rod-mounted) arch bridge. This method involves suspending steel strands at the test section and installing instruments and facilities at the lower end of the strands. Deflection is then measured at the corresponding section using displacement gauges, levels, etc. However, if there are too many measuring points on the arch ring, a large number of steel strands need to be tied, and numerous displacement gauges need to be installed at the ends of the strands, making the operation cumbersome, difficult, and uneconomical. Another example is Chinese invention patent application number 202110420306.2, which provides a method for monitoring arch bridge deflection based on temperature influence correction. This method uses a high-precision measuring robot to collect the height and coordinates of the arch ribs and then calculates the deflection at the measuring points on the arch ring. While this method is good, the high-precision measuring robot is expensive, making the method uneconomical. Summary of the Invention

[0003] In view of the above, it is necessary to provide a test device and method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the small beam. This test device does not require the installation of sensors or other devices on the arch bridge, which simplifies the operation. Moreover, the results obtained by the test method using this test device are highly accurate, thereby greatly improving efficiency and economy.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] An arch bridge arch ring deflection testing device based on beam strain and inclination angle includes a simulated beam, a rigid support device, strain gauges, inclination angle sensors, and a monitoring platform.

[0006] The simulated beam is positioned below the arch bridge under test, parallel to it. The initial end of the simulated beam is fixed to the ground, and the final end is connected to the arch bridge via a rigid support device. Deflection measurement points on the arch bridge are located between the initial and final ends of the simulated beam. The simulated beam is composed of several connected segments, each segment connected to the arch bridge via a rigid support device. Each segment is equipped with an inclination sensor. Each segment is made of a deformable material, while the rigid support device is made of a non-deformable material. In this system, the rigidity of the material used for each segment of the beam is less than that of the material used for the rigid support device; there is a segment of the beam directly opposite the deflection measuring point on the arch bridge under test, and the segment of the beam is also connected to the part of the arch bridge under test where the deflection measuring point is located through the rigid support device; strain gauges are installed on the segment of the beam, between the initial end of the segment of the beam and the rigid support device connecting the deflection measuring point, and also between the end of the segment of the beam and the rigid support device connecting the deflection measuring point; all strain gauges and tilt sensors are connected to the monitoring platform.

[0007] Preferably, one end of the rigid support device is detachably connected to the arch bridge to be tested, and the other end is detachably connected to the small beam.

[0008] Preferably, each rigid support device is perpendicular to the arch bridge and the beam under test, and each coincides with the normal direction of the point on the arch bridge under test where the rigid support device is installed.

[0009] Preferably, two strain gauges are spaced apart between the initial end of the beam and the rigid support device at the part where the deflection measuring point is located.

[0010] Preferably, when the distance between the deflection measuring points at both ends of the arch ring to be measured is less than the length of the small beam, all deflection measuring points are connected on the same segment of the small beam; when the distance between the deflection measuring points at both ends of the arch ring to be measured is greater than the length of the small beam, all deflection measuring points are connected to different segments of the small beam; when any segment of the small beam is connected to more than one deflection measuring point, strain gauges are arranged between two adjacent deflection measuring points on the same segment of the small beam.

[0011] Preferably, the distance between the end of the simulated beam and the deflection measuring point on the arch bridge to be tested near the end of the simulated beam is less than the length of the small beam segment where the end of the simulated beam is located.

[0012] Based on the above-mentioned testing device, the present invention also provides a method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the small beam, comprising the following steps:

[0013] S1: Determine the length of the simulated beam based on the location of the deflection measuring points on the arch ring of the arch bridge to be tested. Then, determine the number of small beams constituting the simulated beam based on the structural dimensions of the arch ring of the arch bridge to be tested. Determine the number of deflection measuring points corresponding to each small beam segment based on the arrangement of the deflection measuring points on the arch bridge to be tested, and then determine the number of strain gauges. Determine the number of tilt sensors based on the number of small beams. Determine the number of rigid support devices based on the number of small beams and the number of deflection measuring points.

[0014] S2: Connect all the small beams to form a simulated beam, and install strain gauges and tilt sensors according to the above-described testing device. Then, take the initial end of the simulated beam, the initial end of the small beam with strain gauges installed, and the location of each strain gauge and tilt sensor as nodes, and measure the horizontal distance between two adjacent nodes. The measured horizontal distance from the initial end to the end of the simulated beam is then denoted as x. i Let i = 1, 2, 3, ...; then, measure the length of each segment of the beam, denoted as L in the direction from the beginning to the end of the simulated beam. j j = 1, 2, 3, ...; and measure the inclination angle of each segment of the beam in the horizontal direction;

[0015] S3: Install and place rigid support devices to install the simulated beam on the arch bridge to be tested through the rigid support devices, and set the simulated beam parallel to the arch ring of the arch bridge to be tested.

[0016] S4: The values ​​measured by the strain gauges and tilt sensors on the simulated beam are transmitted to the monitoring platform. Based on the values ​​measured by the strain gauges and tilt sensors obtained from the monitoring platform, the deflection curves of each segment of the small beam connected to the deflection measuring point are obtained based on the measured values ​​and the data obtained in step S2. Then, the deflection value of each deflection measuring point on the bridge is obtained. The segments of the small beam are separated by the location of the deflection measuring point connected to them.

[0017] Preferably, in step S4, the deflection curves of each segment of the beam are obtained by the following method:

[0018] First, let the small beam at the initial end of the simulated beam be the first segment, and the small beam on which the deflection curve is to be calculated be the j-th segment of the simulated beam. This small beam has n deflection measuring points connected to it, and n+2 strain gauges are installed on it. It is divided into z segments by the deflection measuring points, where z = n+1. Let the deflection curve of each segment of this small beam be y. z ,y z Let y be a cubic function of X, i.e., y z =A z X 3 +B z X 2 +C z X+D zWhere X is the horizontal distance from the end of the z-th segment of the beam to the beginning of the simulated beam, that is, X is equal to the sum of the horizontal distances between all two adjacent nodes between the end node of the z-th segment of the beam and the node where the beginning of the simulated beam is located.

[0019] Secondly, the constants A of the deflection curve are obtained according to the following formula. z B z C z D z Thus, the deflection curves of each segment of the beam are obtained:

[0020] (1) y1(x1)=(L1sinθ1+…+L j-1 sinθ j-1 cosα

[0021] (2)

[0022]

[0023]

[0024] (3)y”1(x1+x2+x3+x4)=y”2(x1+x2+x3+x4);

[0025] y'1(x1+x2+x3+x4)=y'2(x1+x2+x3+x4);

[0026] y1(x1+x2+x3+x4)=y2(x1+x2+x3+x4);

[0027] …

[0028] y” n (x1+x2+…+x 2n+2 )=y” n+1 (x1+x2+…+x 2n+2 )

[0029] y' n (x1+x2+…+x 2n+2 )=y' n+1 (x1+x2+…+x 2n+2 )

[0030] y n (x1+x2+…+x 2n+2 )=y n+1 (x1+x2+…+x 2n+2 )

[0031] (4)y′ n+1 (x1+x2+…+x 2n+4 )=tanθj cosα,

[0032] Where, ε p h is the strain value measured by the p-th strain gauge along the direction from the beginning to the end of the beam. q Let θ be the height of the q-th strain gauge attached to the beam from the beginning to the end, α be the inclination angle of the beam and the horizontal direction for the desired deflection curve, and θ be the height of the strain gauge attached to the beam from the beginning to the end. r Let p, q, and r be the inclination angle values ​​measured by the inclination sensor on the r-th segment of the simulated beam, where p, q, and r are all equal to 1, 2, 3, ...; when j = 1, x1 = 0 and y1(x1) = 0.

[0033] Then, the deflection of the deflection measuring point is obtained based on the deflection curve and the horizontal distance between the deflection measuring point and the initial end of the simulated beam.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] (1) This invention discloses an arch bridge arch ring deflection testing device based on small beam strain and inclination angle. The testing device sets up a simulated beam at a position parallel to the arch ring of the arch bridge to be tested. The simulated beam is spliced ​​together from multiple small beams and connected to the arch bridge to be tested through a rigid support device to realize deflection transmission. In this way, by installing an inclination angle sensor on the small beam and installing strain gauges based on the position of the deflection measuring point, the corresponding strain value and inclination angle value are measured. Then, the deflection curve of the small beam can be calculated by the testing method given by this invention, and the deflection of the deflection measuring point on the arch ring of the arch bridge to be tested can be obtained. The device and the corresponding testing method simplify the operation while achieving high accuracy and greatly improve the testing efficiency.

[0036] (2) The test device and test method of the present invention, compared with the previous method for testing the deflection of the arch ring of an arch bridge, do not require the installation of sensors or other devices on the arch ring. Moreover, for cases with a large number of measuring points on the arch ring, the present invention only needs to set up inexpensive and easy-to-install rigid supports at the measuring points to realize the deflection transmission, which can solve the problems of difficult operation and installation of sensors and other devices and low economic efficiency, and greatly improve efficiency and economy.

[0037] (3) This invention is applicable to a variety of arch bridges, and the device is easy to install and the test method is simple and convenient to calculate, which has high promotion value. Attached Figure Description

[0038] Figure 1 This is a diagram showing the placement of the simulated beams in this invention;

[0039] Figure 2This is a diagram showing the installation positions of the strain gauge and tilt sensor on the beam of the present invention. In the diagram, (a) is the installation position diagram of the strain gauge and tilt sensor when there is one deflection measuring point on the same beam, (b) is the installation position diagram of the strain gauge and tilt sensor when there are two deflection measuring points on the same beam, and (c) is the installation position diagram of the strain gauge and tilt sensor when the two deflection measuring points correspond to different beams.

[0040] Figure 3 This is a diagram showing the arrangement of values ​​during the calculations in this invention;

[0041] Figure 4 This is a midas simulation diagram of Embodiment 1 of the present invention;

[0042] Figure 5 This is the deflection value calculated by midas in Example 1, along with a magnified view of a portion of it;

[0043] Figure 6 This is a midas simulation diagram of Embodiment 2 of the present invention;

[0044] Figure 7 This is the deflection value calculated by midas in Example 2, along with a magnified view of a portion of it.

[0045] Explanation of main component symbols

[0046] In the figure: 1. Small beam; 2. Rigid support device; 3. Strain gauge; 4. Inclination sensor; 5. Deflection measuring point; 6. Arch bridge to be measured. The following detailed embodiments will further illustrate the present invention in conjunction with the above figures. Detailed Implementation

[0047] Please see Figures 1 to 2 In a preferred embodiment of the present invention, the arch bridge arch ring deflection testing device based on beam strain and inclination angle includes a simulated beam, a rigid support device 2, a strain gauge 3, an inclination sensor 4, and a monitoring platform.

[0048] The simulated beam is positioned below the arch bridge 6 to be tested, parallel to it. The initial end of the simulated beam is fixed to the ground, and the final end is connected to the arch bridge 6 via the rigid support device 2. The deflection measuring point 5 on the arch bridge 6 is located between the initial and final ends of the simulated beam. The simulated beam is composed of several segments 1 connected together. The final end of each segment 1 is connected to the arch bridge 6 via the rigid support device 2, and each segment 1 is equipped with an inclination sensor 4. Each segment 1 is made of a deformable material, while the rigid support device 2 is made of a non-deformable material. The rigidity of the material used in a section of the small beam 1 is less than that of the material used in the rigid support device 2; there is a section of the small beam 1 that is directly opposite the deflection measuring point 5 on the arch bridge 6 to be tested, and the small beam 1 is also connected to the part of the arch bridge 6 to be tested where the deflection measuring point 5 is located through the rigid support device 2; strain gauges 3 are installed on the small beam 1, and the strain gauges 3 are located between the initial end of the small beam 1 and the rigid support device 2 where the deflection measuring point 5 is located, and are also located between the end of the small beam 1 and the rigid support device 2 where the deflection measuring point 5 is located; all strain gauges 3 and tilt sensors 4 are connected to the monitoring platform.

[0049] This invention uses a simulated beam parallel to the arch bridge 6 under test and a rigid support device 2 to connect the arch bridge 6 under test to transfer the deformation of the arch bridge 6 under test to the simulated beam, causing the simulated beam to deform. The tilt angle value and strain value are then measured by the tilt angle sensor 4 and strain gauge 3 installed on the simulated beam. Based on the measured data, the deflection curve at the deflection measuring point 5 of the arch bridge 6 under test is calculated, and the deflection value is obtained.

[0050] In this invention, the designed simulated beam does not need to be the same length as the arch bridge 6 under test; it only needs to cover the deflection measuring points 5 set on the arch bridge 6. Preferably, the distance between the end of the simulated beam and the deflection measuring point 5 on the arch bridge 6 near the end of the simulated beam is less than the length of the small beam 1 where the end of the simulated beam is located. That is, the length of the simulated beam is only longer than the position of the farthest deflection measuring point 5, which reduces the amount of construction work and also lowers the manufacturing cost of the device. In addition, when connecting the small beam 1 constituting the simulated direction to the arch bridge 6 under test, it should be as parallel as possible to the arch ring of the arch bridge 6. When selecting the material for the small beam 1, it should have low stiffness and be easy to deform. In this way, the small beam 1 can deform slightly, improving the accuracy of the deflection test.

[0051] Furthermore, this invention achieves deflection transfer through a rigid support device 2. This rigid support device 2 is made of a material with high rigidity and is not easily deformed, so that the deflection deformation of the arch bridge 6 under test is almost completely transferred to the small beam 1 of the simulated beam. This ensures that the deflection of the small beam 1 where the rigid support device 2 is installed is nearly equal to the deflection of the arch ring of the arch bridge 6 under test. Preferably, one end of the rigid support device 2 is detachably connected to the arch bridge 6 under test, and the other end is detachably connected to the small beam 1, facilitating installation and disassembly. The detachable nature of the rigid support device 2 can be achieved through bolts or other connection methods. Furthermore, each rigid support device 2 is perpendicular to both the arch bridge 6 under test and the small beam 1, and each coincides with the normal direction of the point on the arch bridge 6 where the rigid support device 2 is installed, to better achieve the transfer of deflection deformation.

[0052] This invention simplifies the installation process and improves work efficiency by mounting strain gauges 3 and tilt sensors 4 on a simulated beam. Preferably, two strain gauges 3 are spaced apart between the initial end of the small beam 1 and the rigid support device 2 where the deflection measuring points 5 are located. When the distance between the two deflection measuring points 5 on the arch ring to be measured is less than the length of the small beam 1, all deflection measuring points 5 are connected to the same section of the small beam 1. When the distance between the two deflection measuring points 5 on the arch ring to be measured is greater than the length of the small beam 1, all deflection measuring points 5 are separately connected to different sections. On segment 1; when any segment 1 is connected to more than one deflection measuring point 5, strain gauges 3 are arranged between two adjacent deflection measuring points 5 on the same segment 1; that is, considering that the segment 1 needs to be parallel to the arch ring of the arch bridge 6 to be measured, and that there are many deflection measuring points 5 and they are far apart, it is not convenient to install them on the same segment 1. The connection of the deflection measuring points 5 can be distributed on multiple segments 1, and the number of strain gauges 3 set on each segment 1 is determined according to the number of deflection measuring points 5. Preferably, the number of strain gauges 3 is two more than the number of deflection measuring points 5.

[0053] Based on the above-mentioned testing device, the present invention also provides a method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the small beam, comprising the following steps:

[0054] S1: Determine the length of the simulated beam based on the location of the deflection measuring points on the arch ring of the arch bridge to be tested. Then, determine the number of small beams constituting the simulated beam based on the structural dimensions of the arch ring of the arch bridge to be tested. Determine the number of deflection measuring points corresponding to each small beam segment based on the arrangement of the deflection measuring points on the arch bridge to be tested, and then determine the number of strain gauges. Determine the number of tilt sensors based on the number of small beams. Determine the number of rigid support devices based on the number of small beams and the number of deflection measuring points.

[0055] S2: Connect all the small beams to form a simulated beam, and install strain gauges and tilt sensors according to the above-described testing device. Then, take the initial end of the simulated beam, the initial end of the small beam with strain gauges installed, and the location of each strain gauge and tilt sensor as nodes, and measure the horizontal distance between two adjacent nodes. The measured horizontal distance from the initial end to the end of the simulated beam is then denoted as x. i Let i = 1, 2, 3, ..., that is, measure the horizontal distance between the initial end of each segment of the small beam with strain gauges installed and the initial end of the simulated beam; measure the horizontal distance between the initial end of each segment of the small beam with strain gauges installed, the strain gauges arranged sequentially from the initial end to the end of the small beam, the connection point of the deflection measuring point, and the horizontal distance between two adjacent points between the tilt sensors; then, measure the length of each segment of the small beam, which is denoted as L in the direction from the initial end to the end of the simulated beam. j j = 1, 2, 3, ...; and, measure the inclination angle of each segment of the beam in the horizontal direction; see details. Figure 3 ;

[0056] S3: Install and place rigid support devices to install the simulated beam on the arch bridge to be tested through the rigid support devices, and set the simulated beam parallel to the arch ring of the arch bridge to be tested.

[0057] S4: The values ​​measured by the strain gauges and tilt sensors on the simulated beam are transmitted to the monitoring platform. Based on the values ​​measured by the strain gauges and tilt sensors obtained from the monitoring platform, the deflection curves of each segment of the small beam connected to the deflection measuring point are obtained based on the measured values ​​and the data obtained in step S2. Then, the deflection value of each deflection measuring point on the bridge is obtained. The segments of the small beam are separated by the location of the deflection measuring point connected to them.

[0058] In step S4, the deflection curves of each segment of the beam are obtained using the following method:

[0059] First, let the small beam at the initial end of the simulated beam be the first segment, and the small beam on which the deflection curve is to be calculated be the j-th segment of the simulated beam. This small beam has n deflection measuring points connected to it, and n+2 strain gauges are installed on it. It is divided into z segments by the deflection measuring points, where z = n+1. Let the deflection curve of each segment of this small beam be y. z ,y z Let y be a cubic function of X, i.e., y z =A z X 3 +B z X 2 +C z X+D z Where X is the horizontal distance from the end of the z-th segment of the beam to the beginning of the simulated beam, that is, X is equal to the sum of the horizontal distances between all two adjacent nodes between the end node of the z-th segment of the beam and the node where the beginning of the simulated beam is located.

[0060] Secondly, the constants A of the deflection curve are obtained according to the following formula. z B z C z D z Thus, the deflection curves of each segment of the beam are obtained:

[0061] (1) y1(x1)=(L1sinθ1+…+L j-1 sinθ j-1 cosα

[0062] (2)

[0063]

[0064]

[0065] (3)y”1(x1+x2+x3+x4)=y”2(x1+x2+x3+x4);

[0066] y'1(x1+x2+x3+x4)=y'2(x1+x2+x3+x4);

[0067] y1(x1+x2+x3+x4)=y2(x1+x2+x3+x4);

[0068] …

[0069] y” n (x1+x2+…+x 2n+2 )=y” n+1 (x1+x2+…+x 2n+2 )

[0070] y' n (x1+x2+…+x 2n+2 )=y' n+1 (x1+x2+…+x 2n+2 )

[0071] y n (x1+x2+…+x 2n+2 )=y n+1 (x1+x2+…+x 2n+2 )

[0072] (4)y′ n+1 (x1+x2+…+x 2n+4 )=tanθ j cosα,

[0073] Where, ε p h is the strain value measured by the p-th strain gauge along the direction from the beginning to the end of the beam.q Let θ be the height of the q-th strain gauge attached to the beam from the beginning to the end, α be the inclination angle of the beam and the horizontal direction for the desired deflection curve, and θ be the height of the strain gauge attached to the beam from the beginning to the end. r Let p, q, and r be the inclination angle values ​​measured by the inclination sensor on the r-th segment of the simulated beam, where p, q, and r are all equal to 1, 2, 3, ...; when j = 1, x1 = 0 and y1(x1) = 0.

[0074] Then, based on the deflection curve and the distance between the deflection measuring point and the initial end of the simulated beam, the deflection at that measuring point is calculated, i.e., the deflection at the nth measuring point of the actual bridge = y n (x n )=y n+1 (x n ).

[0075] The above calculation formula is based on the following principle:

[0076] Given that the simply supported beam M(X) is always a linear function of x, the bridge deflection y is always a cubic function of x. Based on existing calculation formulas:

[0077]

[0078] y′=tanθ

[0079]

[0080] In the above formulas: M(x) is the bridge bending moment formula; EI is the stiffness; θ is the inclination angle corresponding to position x; ε(x) is the strain value at position x; h x The height of the point where the strain value at x is obtained is the distance from the top of the beam.

[0081] Based on the above three calculation formulas, and given that the deflection y, slope y′, and curvature y″ at both ends of the rigid support device are the same, the rigid support device has high stiffness and is not easily deformed. The deflection at the end of the beam segment at the measuring point can be regarded as the stiffness of multiple beam segments before the measuring point multiplied by its end inclination angle. Furthermore, the strain can be measured by strain gauges, and the slope y′ can be obtained. By combining the above conditions, the new formula given by this invention can be obtained.

[0082] Example 1

[0083] Based on the above-mentioned arch bridge arch ring deflection testing device and method, in order to verify the feasibility of the present invention, the following embodiments are provided (the embodiments take a simulated beam with 4 small beams and 1 deflection measuring point as an example, i.e., j=4, n=1), specifically including the following:

[0084] A bridge with an 8-meter span and a 2.5-meter arch height was constructed using Midas software. The bridge was fixed at both ends, and loads were applied to the bridge. Simulated beams were placed 20cm below the bridge, with the smaller beams parallel to the arch. Based on the slope variation of the arch (a section of smaller beam was placed parallel to the length with a small slope variation) and the location of the measuring points, four smaller beams were constructed. The initial ends of the simulated beams were simply supported, and the ends of the remaining smaller beams were connected to the arch ring via rigid support devices. A deflection measuring point was set on the arch ring parallel to the fourth smaller beam, 2.72m from the initial end (leftmost) of the fourth smaller beam. Furthermore, the section of the arch ring at this deflection measuring point was also connected to the fourth smaller beam via rigid support devices. See [link to specific details] for details. Figure 4 In addition, the beam is set to a square cross-section with a side length of 0.2m, and the stress value is located at the center. Therefore, the height of the strain value obtained by each strain gauge on the beam from the top of the beam is h = 0.1m.

[0085] The deflection results obtained after calculation using the Midas software are as follows: Figure 5 As shown. By Figure 5 It can be seen that the deflection at the measuring point on the arch ring of the arch bridge is 0.002 mm, and the deflection at the corresponding point on the small beam connected by the rigid support device is also 0.002 mm. The following are the deflection curves and deflections at the corresponding points on the small beam connected by the rigid support device calculated by the test method of this invention, as detailed below:

[0086] As shown above, one deflection measuring point can divide the fourth segment of the beam into two segments. The deflection curve of each segment is a cubic function of X, that is,

[0087]

[0088] Substituting the calculation formula provided by the testing method of this invention, the calculation formula for one deflection measuring point on the bridge can be obtained as follows:

[0089] (1)y1(x1)=(L1sinθ1+L2sinθ2+L3sinθ3)cosα

[0090] (2)

[0091]

[0092] (3)y”1(x1+x2+x3+x4)=y”2(x1+x2+x3+x4)

[0093] y'1(x1+x2+x3+x4)=y'2(x1+x2+x3+x4)

[0094] y1(x1+x2+x3+x4)=y2(x1+x2+x3+x4)

[0095] (4)y'2(x1+x2+x3+x4+x5+x6)=tanθ4cosα

[0096] Where, L1 = 0.97m, L2 = 1.09m, L3 = 0.9m, x1 = 2.44m, x2 = 0.07m, x3 = 0.14m, x4 = 0.07m, x5 = 0.14m, x6 = 0.14m, h1 = h2 = h3 = 0.1m, θ1 = 3.2 × 10 -5 θ2=3.8×10 -5 θ3=4.1×10 -5 θ4=1.635×10 -4 α = 30 degrees (clockwise is positive). We obtain...

[0097] A1 = -5.355 × 10 -10 B1 = 7.4476 × 10 -10 C1 = 1.2461 × 10 -6 D1 = -1.3841 × 10 -6 ,

[0098] A2 = -0.1659 × 10 -8 B2 = 0.99125 × 10 -8 C2 = 1.2212 × 10 -6 D2 = -1.362 × 10 -6 ,

[0099] Therefore, the deflection value at the deflection measuring point is y1(2.72)=0.002mm≈y2(2.72)=0.0019996mm.

[0100] As mentioned above, the deflection at the measuring point on the bridge under test, calculated using Midas software, is 0.002 mm, and the corresponding deflection at the point on the small beam connected by the rigid support device is also 0.002 mm. The deflection calculated by the formula of this invention is approximately 0.002 mm, which is basically consistent with the result obtained from the Midas software calculation. Therefore, the calculation results of the testing device and method proposed in this invention are considered to have high accuracy and feasibility.

[0101] Example 2

[0102] The present invention also provides a second embodiment, in which the simulated beam consists of 4 small beam segments and 2 deflection measuring points, i.e., j=4 and n=2, specifically including the following:

[0103] Similar to Example 1 with one deflection measuring point, the same simulation model is established and the same load is applied. The difference between this example and Example 1 is that two deflection measuring points are set on the arch ring parallel to the fourth beam segment. Deflection measuring point 1 is 2.72m from the beginning (leftmost) of the fourth beam segment, and deflection measuring point 2 is 2.8m from the leftmost point. The specific structure described above is as follows: Figure 6 As shown.

[0104] The deflection results obtained after calculation using the Midas software are as follows: Figure 7 As shown. By Figure 7 It can be seen that the deflection at point 1 on the arch ring of the arch bridge is 0.002 mm, and the deflection at the corresponding point on the small beam connected by the rigid support device is 0.002 mm. Since the distance difference is not large, the deflection at point 2 on the arch ring of the arch bridge is 0.002 mm, and the deflection at the corresponding point on the small beam connected by the rigid support device is 0.002 mm. The following are the deflection curves and deflections at the corresponding points on the small beam connected by the rigid support device calculated by the test method of the present invention, as follows:

[0105] As shown above, the two deflection measurement points divide the fourth segment of the beam into two segments. The deflection curve of each segment is a cubic function of X, that is,

[0106]

[0107] Substituting the calculation formula provided by the test method of this invention, the calculation formula for the two deflection measuring points on the bridge can be obtained as follows:

[0108] (1)y1(x1)=(L1sinθ1+L2sinθ2+L3sinθ3)cosα

[0109] (2)

[0110]

[0111]

[0112] (3)y”1(x1+x2+x3+x4)=y”2(x1+x2+x3+x4)

[0113] y'1(x1+x2+x3+x4)=y'2(x1+x2+x3+x4)

[0114] y1(x1+x2+x3+x4)=y2(x1+x2+x3+x4)

[0115] y”2(x1+x2+x3+x4+x5+x6)=y”3(x1+x2+x3+x4+x5+x6)

[0116] y'2(x1+x2+x3+x4+x5+x6)=y'3(x1+x2+x3+x4+x5+x6)

[0117] y2(x1+x2+x3+x4+x5+x6)=y3(x1+x2+x3+x4+x5+x6)

[0118] (4)y3'(x1+x2+x3+x4+x5+x6+x7+x8)=tanθ4cosα

[0119] Where, L1 = 0.97m, L2 = 1.09m, L3 = 0.9m, x1 = 2.44m, x2 = 0.07m, x3 = 0.14m, x4 = 0.07m, x5 = 0.14m, x6 = 0.14m, x7 = 0.1m, x8 = 0.1m, h1 = h2 = h3 = h4 = 0.1m. θ1 = 3.2 × 10 -5 θ2=3.8×10 -5 θ3=4.1×10 -5 θ4=8.172×10 -4 α = 30 degrees (clockwise is positive). We obtain...

[0120] A1 = -5.355 × 10 -10 B1 = 7.4476 × 10 -10 C1 = 1.2461 × 10 -6 D1 = -1.3841 × 10 -6 ,

[0121] A2 = -0.1659 × 10 -8 B2 = 0.99125 × 10 -8 C2 = 1.2212 × 10 -6 D2 = -1.362 × 10 -6 ,

[0122] A3 = -2.2355 × 10 -9 B3 = 1.4755 × 10 -8 C3 = 1.207 × 10 -6 D3 = -1.356 × 10 -6 ,

[0123] Therefore, the deflection values ​​at the deflection measurement points are y1(2.72)=0.002mm≈y2(2.72)=0.0019996mm, y2(2.8)=0.0020987mm≈y3(2.8)=0.0020902mm.

[0124] As can be seen from the above, the deflection of the bridge under test at point 1 was calculated to be 0.002 mm using the Midas software, and the deflection calculated by the formula of this invention is approximately 0.002 mm. The deflection of the bridge under test at point 2 was calculated to be 0.002 mm using the Midas software, and the deflection calculated by the formula of this invention is approximately 0.002099 mm, with an error of 4.7%. The above calculation errors are all less than 5%, so it is considered that the device and calculation method proposed in this invention are correct and highly accurate.

[0125] Finally, it should be noted that when there are a large number of deflection measurement points on the beam, the deflection of each segment of the beam can be obtained by using MATLAB matrix method, thereby obtaining the deflection of each deflection measurement point on the bridge.

[0126] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. A method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the small beam, characterized in that, The arch ring deflection of the arch bridge was tested using a test device based on the strain and inclination angle of the small beam. The test device includes a simulated beam, a rigid support device, strain gauges, inclination sensors, and a monitoring platform. The simulated beam is positioned below the arch ring of the bridge under test, parallel to it. The initial end of the simulated beam is fixed to the ground, and the final end is connected to the arch ring via a rigid support device. The deflection measurement point on the arch ring is located between the initial and final ends of the simulated beam. The simulated beam is composed of several connected segments, each segment connected to the arch ring via a rigid support device. Each segment is equipped with an inclination sensor. Each segment is made of a deformable material, while the rigid support device is made of a non-deformable material. In terms of material fabrication, the rigidity of the material used for each segment of the beam is less than that of the material used for the rigid support device; there is a segment of the beam directly opposite the deflection measuring point on the arch ring of the arch bridge under test, and the segment of the beam is also connected to the part of the arch ring of the arch bridge under test where the deflection measuring point is located through the rigid support device; strain gauges are installed on the segment of the beam, between the initial end of the segment of the beam and the rigid support device connecting the deflection measuring point, and also between the end of the segment of the beam and the rigid support device connecting the deflection measuring point; all strain gauges and tilt sensors are connected to the monitoring platform; The testing method includes the following steps: S1: Determine the length of the simulated beam based on the location of the deflection measuring points on the arch ring of the arch bridge to be tested. Then, determine the number of small beams constituting the simulated beam based on the structural dimensions of the arch ring of the arch bridge to be tested. Determine the number of deflection measuring points corresponding to each small beam segment based on the arrangement of the deflection measuring points on the arch ring of the arch bridge to be tested, and then determine the number of strain gauges. Determine the number of tilt sensors based on the number of small beams. Determine the number of rigid support devices based on the number of small beams and the number of deflection measuring points. S2: All small beams are connected to form a simulated beam, and strain gauges and tilt sensors are installed according to the test device. Then, the initial end of the simulated beam, the initial end of the small beam with strain gauges installed, each deflection measurement point on the small beam for which the deflection curve is to be obtained, and the location of each strain gauge and tilt sensor are all taken as nodes. The horizontal distance between two adjacent nodes is measured, and the measured horizontal distance from the initial end to the end of the simulated beam is set sequentially as follows: , Among them, horizontal spacing The distance from the initial end of the simulated beam to the initial end of the smaller beam whose deflection curve is to be obtained is used; then, the length of each smaller beam segment is measured, and this length is sequentially set from the initial end to the final end of the simulated beam as... , And, measure the inclination angle of each segment of the beam in the horizontal direction; S3: Install and place rigid support devices to install the simulated beam on the arch ring of the arch bridge to be tested through the rigid support devices, and set the simulated beam parallel to the arch ring of the arch bridge to be tested. S4: The values ​​measured by the strain gauges and tilt sensors on the simulated beam are transmitted to the monitoring platform. Based on the values ​​measured by the strain gauges and tilt sensors obtained by the monitoring platform, the deflection curves of each segment of the small beam connected to the deflection measuring point are obtained based on the measured values ​​and the data obtained in step S2. Then, the deflection value of each deflection measuring point on the bridge is obtained. The segments of the small beam are separated by the location of the deflection measuring point connected to them. In step S4, the deflection curves of each segment of the beam are obtained using the following method: First, let the small beam at the initial end of the simulated beam be the first small beam, and the small beam for which the deflection curve is obtained be the first small beam of the simulated beam. Duan Xiaoliang, the small beam is connected to There are several deflection measuring points, on which are set up... Each strain gauge is divided into several sections by deflection measurement points. Each segment, The deflection curve of each segment of the small beam is set as follows: , Let f be a cubic function of f, that is, ,in, For Xiao Liang The horizontal distance from the end of each segment to the beginning of the simulated beam, i.e. Equal to Xiao Liang's The sum of the horizontal distances between all two adjacent nodes from the end node of a segment to the node where the beginning of the simulated beam is located; Secondly, the constants of the deflection curve are obtained according to the following formula. , , , Thus, the deflection curves of each segment of the beam are obtained: ， in, For the small beam, the direction from the initial end to the end is the first The strain value measured by each strain gauge For the small beam, the direction from the initial end to the end is the first The height of the strain gauge attachment point from the top of the beam Let the small beam be the beam whose deflection curve is to be calculated, and the inclination angle in the horizontal direction be given. To simulate the first beam The tilt angle value measured by the tilt sensor on the beam segment. ;when hour, , ; Then, the deflection of the deflection measuring point is obtained based on the deflection curve and the horizontal distance between the deflection measuring point and the initial end of the simulated beam.

2. The method for testing the deflection of an arch bridge ring based on the strain and inclination angle of a small beam as described in claim 1, characterized in that: One end of the rigid support device is detachably connected to the arch ring of the arch bridge to be tested, and the other end is detachably connected to the small beam.

3. The method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the small beam as described in claim 1, characterized in that: Each rigid support device is perpendicular to the arch ring and beam of the arch bridge under test, and all of them coincide with the normal direction of the point on the arch ring of the arch bridge under test where the rigid support device is set.

4. The method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the small beam as described in claim 1, characterized in that: Two strain gauges are spaced apart between the initial end of the beam and the rigid support device at the part where the deflection measurement point is located. The rigid support device is one closer to the initial end of the beam.

5. The method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the small beam as described in claim 1, characterized in that: When the distance between the two ends of the deflection measuring points on the arch ring of the bridge under test is less than the length of the small beam, all deflection measuring points are connected on the same segment of the small beam; when the distance between the two ends of the deflection measuring points on the arch ring of the bridge under test is greater than the length of the small beam, all deflection measuring points are connected to different segments of the small beam; when any segment of the small beam is connected to more than one deflection measuring point, strain gauges are arranged between two adjacent deflection measuring points on the same segment of the small beam.

6. The method for testing the deflection of the arch ring of an arch bridge based on the strain and inclination angle of the small beam as described in claim 1, characterized in that: The distance between the end of the simulated beam and the deflection measuring point on the arch ring of the bridge under test near the end of the simulated beam is less than the length of the small beam segment where the end of the simulated beam is located.

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