Method for measuring force of horizontal cable of arch bridge

Abstract

The application discloses a kind of arch bridge horizontal cable tension measuring method, comprising the following steps: installing horizontal cable;Three temperature observation points are selected on horizontal cable;Respectively install an observation prism of total station on the arch structure near the anchor head of the two ends of horizontal cable, and are respectively set as first displacement measuring point and second displacement measuring point;Initial tension horizontal cable obtains the initial tension of horizontal cable;Immediately measure the relative distance between first displacement measuring point and second displacement measuring point by total station after initial tension of horizontal cable is completed;The temperature of three temperature measuring points on horizontal cable is measured simultaneously;When measuring the cable tension at any time, the relative distance between first displacement measuring point and second displacement measuring point is measured by total station, and the temperature of three temperature measuring points is measured simultaneously;Calculate the cable tension at any time after initial tension;When tensioning horizontal cable again, record the amount of anchor head pulling out;Calculate the cable tension at the moment of tensioning again.The application has the characteristics of simple and fast, and can be measured at any time.

Description

Technical Field

[0001] This invention relates to a method for measuring the horizontal cable force of an arch bridge. Background Technology

[0002] Methods for measuring cable force generally include: pressure gauges, pressure sensors, frequency methods, magnetic flux methods, fiber optic grating vibration methods, and video image vibration measurement methods. Pressure gauges typically measure pressure values ​​when horizontal cables are tensioned using hydraulic equipment. Pressure sensors utilize the strain gauge method; representative instruments include cable gauges. Due to the high cost of pressure sensors and the need for supporting monitoring systems, their use on permanent cables during bridge operation is somewhat limited. The frequency method is the most commonly used method for cable force measurement. This method uses accelerometers and analysis systems to measure the natural frequency of the cable caused by environmental excitation, thereby calculating the cable force. However, this method is also affected by cable sag, temperature, boundary conditions, etc., which can introduce measurement errors. The video image vibration measurement method uses a video image sensing system to measure the dynamic response data of the cable, and uses data analysis software to identify the mode shape and frequency of the cable, thus obtaining the cable force. This method essentially uses the frequency method for cable force measurement. Pressure sensors and cable gauges, among other measurement methods, utilize the principle of vibrating wire strain gauges. A number of vibrating wire sensors are arranged inside the instrument, and the strain change is measured by measuring the frequency of the vibrating wire, thereby calculating the cable force. However, the measured values ​​are significantly affected by temperature.

[0003] All of the above measurement methods require certain measuring instruments and professional measurement personnel for data analysis. Furthermore, the measurement costs are high, the measurement cycle is long, and it is not conducive to obtaining data quickly on-site. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for measuring the horizontal cable force of an arch bridge. This method is simple, quick, allows for measurement at any time, and has high accuracy, thus meeting construction requirements.

[0005] The objective of this invention is achieved as follows: a method for measuring the horizontal cable force of an arch bridge, comprising the following steps:

[0006] Step 1: Insert both ends of the horizontal cable into the anchor heads fixed on the arch structure to complete the installation of the horizontal cable;

[0007] Step 2: Select three locations on the horizontal cable as temperature observation points. The three temperature observation points are the middle of the horizontal cable and both ends of the horizontal cable.

[0008] Step 3: Install a total station observation prism on the arch structure near the anchor heads at both ends of the horizontal cable, and set it as the first displacement measuring point and the second displacement measuring point respectively.

[0009] Step 4: Use the jacks at both ends of the horizontal cable to initially tension the horizontal cable and obtain the initial tension force F0 of the horizontal cable;

[0010] Step 5: After the initial tensioning of the horizontal cable is completed, immediately measure the relative distance L0 between the first displacement measuring point and the second displacement measuring point using the observation prisms of two total stations; at the same time, measure the temperature of three temperature observation points on the horizontal cable and calculate the arithmetic mean t0 of the temperature of the three temperature observation points.

[0011] Step 6: When measuring the cable force of the horizontal cable at any time, measure the relative distance L between the first displacement measuring point and the second displacement measuring point through the observation prisms of two total stations, and at the same time measure the temperature of the three temperature observation points, and calculate the arithmetic mean t of the temperature of the three temperature observation points.

[0012] Step 7: Calculate the cable force F of the horizontal cable at any time after the initial tensioning using the following formula (1):

[0013]

[0014] In formula (1): Vx is the relative position increment of the anchor points at both ends of the horizontal cable, Vx = L - L0; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of ​​the horizontal cable; E and A are obtained by referring to the quality assurance certificate parameters of the horizontal cable material; α s The coefficient of thermal expansion of the horizontal cable material was obtained by consulting the relevant specifications.

[0015] Step 8: When tensioning the horizontal cable again, record the pull-out amount Vl of the horizontal cable anchor head during tensioning;

[0016] Step nine, calculate the cable force F of the horizontal cable at the moment of re-tensioning using the following formula (2):

[0017]

[0018] In formula (2): Vx = L - L0; Vl is the pull-out amount of the horizontal cable anchor head; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of ​​the horizontal cable; E and A are obtained by referring to the quality assurance certificate parameters of the horizontal cable material; α s The coefficient of thermal expansion of the horizontal cable material is obtained by referring to the standard.

[0019] In the above-mentioned method for measuring the horizontal cable force of an arch bridge, formulas (1) and (2) are derived after considering the following factors that affect the cable force during steps seven and nine:

[0020] A. The location of the anchor point: Since the horizontal cable is in a catenary state under its own weight, its shape is considered to be approximately a quadratic parabola. The length S of the horizontal cable is calculated using the parabola formula:

[0021]

[0022] In the above formula:

[0023] fm is the mid-span normal deflection of the horizontal cable:

[0024]

[0025] q is the unit weight of the horizontal cable;

[0026] T is the tension at the center of the horizontal cable;

[0027] l is the distance between the two anchor points of the horizontal cable;

[0028] α is the horizontal inclination angle of the horizontal cable;

[0029] The length S of the horizontal cable can be obtained from the above two equations:

[0030]

[0031] Since the weight of the horizontal cable is very small relative to the cable force, the second term in the above equation can be ignored. The length of the horizontal cable is approximately S = l;

[0032] The change in the anchorage position of the horizontal cable is equivalent to the change in cable length. When the increment in the anchorage position is Vx, the cable force of the horizontal cable is:

[0033]

[0034] B. Temperature changes: When the temperature changes, the cable force will change due to thermal expansion and contraction, and the change in cable force will be directly reflected in the change in cable length.

[0035] When the change in temperature is Δt, the change in cable length is ΔL = α s sΔt;

[0036] The change in cable force in the horizontal cable is ΔF = ΔσA = EAΔε = EAα s Δt

[0037] In the above formula: Δσ is the stress change of the horizontal cable; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of ​​the horizontal cable; Δε is the strain change of the horizontal cable; α s The coefficient of thermal expansion of the horizontal cable material;

[0038] C. Anchor pull-out: When the horizontal cable is tensioned, the anchor pull-out changes, which in turn leads to changes in the cable force. The anchor pull-out and the displacement of the anchor point together change the cable length. The effects of the anchor pull-out and the displacement of the anchor point on the cable force are consistent. Assuming that the total increase in the anchor pull-out at both ends of the horizontal cable is Vl, the following formula for calculating the cable force corrected by the anchor pull-out at any given time is obtained:

[0039]

[0040] D. Considering factors A, B, and C above

[0041] When the initial tension of the horizontal cable is F0, the temperature is t0, and the distance between the anchor points at both ends of the horizontal cable is L0, and the horizontal cable is tensioned again at a certain working condition temperature t after the initial tension, with the relative position increment of the anchor points at both ends of the horizontal cable being Vx and the pull-out amount of the anchor head being Vl, then the cable force of the horizontal cable in this state is:

[0042]

[0043] The method for measuring the horizontal cable force of an arch bridge according to the present invention has the following characteristics:

[0044] 1. This invention considers the relationship between cable force, cable length, temperature, and anchor head pull-out amount; by installing position measuring instruments at the anchor points at both ends of the horizontal cable to measure the relative positions of the anchor points at different times, the length change of the horizontal cable is calculated; by selecting three positions on the horizontal cable as temperature observation points to measure the temperature value of the horizontal cable at any time, the average temperature of the horizontal cable at any time is obtained, and then the cable length change with temperature is obtained.

[0045] 2. The measurement method of the present invention is simple and quick, does not require special instruments or professional personnel to perform the measurement. Surveyors can use conventional measuring instruments such as total stations to measure at any time, and the accuracy is high, which meets the construction requirements of arch bridges. Attached Figure Description

[0046] Figure 1 This is a state diagram of step four in the method for measuring the horizontal cable force of an arch bridge according to the present invention. Detailed Implementation

[0047] The invention will now be further described with reference to the accompanying drawings.

[0048] Please see Figure 1 The method for measuring the horizontal cable force of an arch bridge according to the present invention includes the following steps:

[0049] Step 1: Insert both ends of the horizontal cable 10 into the anchor heads fixed on the arch structure 100 to complete the installation of the horizontal cable 10.

[0050] Step 2: Install a total station observation prism on the arch structure 100 near the anchor heads at both ends of the horizontal cable 10, and set it as the first displacement measuring point 11 and the second displacement measuring point 12, respectively, to measure the distance between the two anchor points of the horizontal cable 10.

[0051] Step 3: Select three locations on the horizontal cable 10 as temperature observation points 1B. The three temperature observation points 1B are the middle part and both ends of the horizontal cable 10, respectively, to measure the temperature of the horizontal cable 10.

[0052] Step 4: According to the construction requirements, use the jacks 20 at both ends of the horizontal cable to initially tension the horizontal cable 10, and obtain the initial tension force F0 of the horizontal cable 10.

[0053] Step 5: After the initial tensioning of the horizontal cable is completed, immediately measure the relative distance L0 between the first displacement measuring point and the second displacement measuring point through the observation prisms of two total stations. At the same time, measure the initial temperature of three temperature observation points on the horizontal cable and calculate the arithmetic mean t0 of the initial temperature of the three temperature observation points.

[0054] Step 6: When measuring the cable force of the horizontal cable at any time, measure the relative distance L between the first displacement measuring point and the second displacement measuring point through the observation prism of the two total stations, and at the same time measure the temperature of the three temperature measuring points, and calculate the arithmetic mean t of the temperature of the three temperature observation points.

[0055] Step 7: Calculate the cable force F of the horizontal cable at any time after the initial tensioning using the following formula (1):

[0056]

[0057] In formula (1), Vx is the relative position increment of the anchor points at both ends of the horizontal cable, Vx = L - L0; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of ​​the horizontal cable; E and A are obtained by referring to the quality assurance certificate parameters of the horizontal cable material; α s The coefficient of thermal expansion of the horizontal cable material was obtained by consulting the relevant specifications.

[0058] Step 8: When tensioning the horizontal cable again, record the pull-out amount Vl of the horizontal cable anchor head during tensioning;

[0059] Step nine, calculate the cable force F of the horizontal cable at the moment of re-tensioning using the following formula (2):

[0060]

[0061] In formula (2), Vx is the relative position increment of the anchor points at both ends of the horizontal cable, Vx = L - L0; Vl is the pull-out amount of the horizontal cable anchor head; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of ​​the horizontal cable; E and A are obtained by referring to the quality assurance certificate parameters of the horizontal cable material; α s The coefficient of thermal expansion of the horizontal cable material is obtained by referring to the standard.

[0062] Formulas (1) and (2) are derived after considering the following factors that affect the cable force:

[0063] A. The location of the anchor point: Since the horizontal cable is in a catenary state under its own weight, its shape is considered to be approximately a quadratic parabola. The length S of the horizontal cable is calculated using the parabola formula:

[0064]

[0065] In the above formula:

[0066] fm is the mid-span normal deflection of the horizontal cable:

[0067]

[0068] q is the unit weight of the horizontal cable;

[0069] T is the tension at the center of the horizontal cable;

[0070] l is the distance between the two anchor points of the horizontal cable;

[0071] α is the horizontal inclination angle of the horizontal cable;

[0072] The length S of the horizontal cable can be obtained from the above two equations:

[0073]

[0074] Since the weight of the horizontal cable is very small relative to the cable force, the second term in the above equation can be ignored. The length of the horizontal cable is approximately S = l;

[0075] The change in the position of the two anchor points of the horizontal cable is equivalent to the change in the cable length. When the increment of the change in the anchor point position is Vx, the cable force of the horizontal cable is:

[0076]

[0077] B. Temperature changes: When the temperature changes, the cable force will change due to thermal expansion and contraction, and the change in cable force will be directly reflected in the change in cable length.

[0078] When the change in temperature is Δt, the change in cable length is ΔL = α s sΔt;

[0079] The change in cable force in the horizontal cable is ΔF = ΔσA = EAΔε = EAα s Δt

[0080] In the above formula: Δσ is the stress change of the horizontal cable; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of ​​the horizontal cable; Δε is the strain change of the horizontal cable; α s The coefficient of thermal expansion of the horizontal cable material;

[0081] C. Anchor pull-out: When the horizontal cable is tensioned, the anchor pull-out changes, which in turn leads to changes in the cable force. The anchor pull-out and the displacement of the anchor point together change the cable length. The effects of the anchor pull-out and the displacement of the anchor point on the cable force are consistent. When the total increase in the anchor pull-out at both ends of the horizontal cable is Vl, the following formula for calculating the cable force corrected by the anchor pull-out at any given time is obtained:

[0082]

[0083] D. Considering factors A, B, and C above

[0084] When the initial tension of the horizontal cable is F0, the temperature is t0, and the distance between the anchor points at both ends of the horizontal cable is L0, and the horizontal cable is tensioned again at a certain working condition temperature t after the initial tension, with the relative position increment of the anchor points at both ends of the horizontal cable being Vx and the pull-out amount of the anchor head being Vl, then the cable force of the horizontal cable in this state is:

[0085]

[0086] The measurement method of this invention will now be illustrated using the Qingshuitang Bridge as an example. This arch bridge is a mid-span steel truss arch bridge with four horizontal cables. The initial distance L0 between the anchorage points at both ends of the four horizontal cables is 477.805m, and the cross-sectional area A of each horizontal cable is 10891mm². 2 The elastic modulus E of the horizontal cable is 1.9 × 10⁻⁶. 5 MPa, the coefficient of thermal expansion α of the horizontal cable material s Take 1.2 × 10 -5 / ℃. According to the construction requirements, each horizontal cable was initially tensioned, and the initial tension force F0 and initial temperature t0 of each horizontal cable were measured. At time 1, time 2 and time 3 during the construction period after the initial tensioning, each horizontal cable was tensioned again. At time 1, time 2 and time 3, the pull-out amount Vl of the anchor head, the relative position increment Vx of the two anchor points and the temperature t of each horizontal cable were measured. Then, the cable force of each horizontal cable at time 1, time 2 and time 3 was calculated by formula (2) of this invention. The result was compared with the actual tension force of each horizontal cable at time 1, time 2 and time 3. The error rate was less than 1%. The specific measured and calculated values ​​are shown in Table 1 below:

[0087] Table 1

[0088]

[0089] The above embodiments demonstrate that the measurement method of the present invention has high accuracy, provides a theoretical basis for the tension force applied when tensioning horizontal cables, and meets the needs of on-site construction.

[0090] The above embodiments are for illustrative purposes only and are not intended to limit the invention. Those skilled in the art can make various changes or modifications without departing from the spirit and scope of the invention. Therefore, all equivalent technical solutions should also fall within the scope of the invention and should be defined by the claims.

Claims

1. A method for measuring the force of a horizontal cable of an arch bridge, characterized by, The method comprises the following steps: Step one, insert the two ends of the horizontal cable into the anchor head fixed on the arch structure, complete the installation of the horizontal cable; Step two, select three positions on the horizontal cable as temperature observation points, the three temperature observation points are the middle part of the horizontal cable and the two ends of the horizontal cable respectively; Step three, install an observation prism of a total station instrument on the arch structure near the anchor head at the two ends of the horizontal cable respectively, and set them as the first displacement measuring point and the second displacement measuring point respectively; Step four, use the jacks at the two ends of the horizontal cable to initially tension the horizontal cable, and obtain the initial tension force F0 of the horizontal cable; Step five, after the initial tension of the horizontal cable is completed, immediately measure the relative distance L0 between the first displacement measuring point and the second displacement measuring point through the observation prisms of the two total station instruments; meanwhile, measure the temperatures of the three temperature observation points on the horizontal cable, and calculate the arithmetic mean value t0 of the temperatures of the three temperature observation points; Step six, when measuring the cable force of the horizontal cable at any time, measure the relative distance L between the first displacement measuring point and the second displacement measuring point through the observation prisms of the two total station instruments, and measure the temperatures of the three temperature observation points, and calculate the arithmetic mean value t of the temperatures of the three temperature observation points; Step seven, calculate the cable force F of the horizontal cable at any time after the initial tension through the following formula (1): In formula (1), Vx is the relative position increment of the anchoring points at both ends of the horizontal cable, Vx = L - L0; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of the horizontal cable; E and A are obtained by consulting the parameters of the quality assurance book of the horizontal cable material; α s is the temperature expansion coefficient of the horizontal cable material, which is obtained by consulting the specification; Step eight, when tensioning the horizontal cable again, record the pulling-out amount Vl of the anchor head of the horizontal cable at the time of tensioning; Step nine, calculate the cable force F of the horizontal cable at the time of tensioning again through the following formula (2): In formula (2): Vx=L-L0; Vl is the pull-out amount of the horizontal cable anchor head; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of the horizontal cable; E and A are obtained by consulting the parameters of the quality assurance book of the horizontal cable material; α s is the temperature expansion coefficient of the horizontal cable material, which is obtained by consulting the specification.

2. The method of measuring the force of the horizontal cable of an arch bridge according to claim 1, wherein When steps seven and nine are performed, the formula (1) and the formula (2) are derived by considering the following factors which have an influence on the cable force: A. The position of the anchoring point, since the current state of the horizontal cable under the action of the dead weight is catenary, it is considered that the shape of the horizontal cable is approximately a quadratic parabola, and the cable length S of the horizontal cable is calculated according to the parabola formula: In the above formula: fm is the mid-span normal deflection of the horizontal cable; q is the unit weight of the horizontal cable; T is the tension at the central position of the horizontal cable; l is the distance between the anchoring points at the two ends of the horizontal cable; α is the horizontal inclination angle of the horizontal cable; The cable length S of the horizontal cable is obtained from the above two formulas: Since the self-weight of the horizontal cable is very small relative to the cable force, the second term in the above equation is ignored The cable length of the horizontal cable is approximately S = l; The change amount of the position of the anchoring point of the horizontal cable is equivalent to the change amount of the cable length, when the incremental amount of the position of the anchoring point is Vx, and the cable force of the horizontal cable is: B. The change of temperature, when the temperature changes, the cable force will change due to thermal expansion and contraction, and the change of the cable force will also directly reflect the change of the cable length; When the amount of change in temperature is Δt, the amount of change in the length of the cable is ΔL = α s sΔt; The amount of change in the cable force of the horizontal cable is ΔF = ΔσA = EAΔε = EAα s Δt In the above formula: Δσ is the stress change value of the horizontal cable; E is the elastic modulus of the horizontal cable; A is the cross-sectional area of the horizontal cable; Δε is the strain change value of the horizontal cable; α s is the temperature expansion coefficient of the horizontal cable material; C. The pulling-out amount of the anchor head, when the horizontal cable is tensioned, the pulling-out amount of the anchor head will change, which will also cause the change of the cable force; the pulling-out amount of the anchor head and the displacement of the anchoring point jointly change the cable length, and the influence effect of the pulling-out amount of the anchor head and the displacement of the anchoring point on the cable force is consistent, it is assumed that the pulling-out amount of the anchor head at the two ends of the horizontal cable is increased by Vl, and the following formula for calculating the cable force of the anchor head pulling-out amount correction at any time is obtained: D. Comprehensive consideration of the above factors A, B and C When the initial tension force of the horizontal cable is F0, the temperature is t0, the distance between the anchoring points at the two ends of the horizontal cable is L0, the temperature at a certain working condition after the initial tension of the horizontal cable is t, the horizontal cable is tensioned again, the relative position incremental amount of the anchoring points at the two ends of the horizontal cable is Vx, and the pulling-out amount of the anchor head is Vl, then the cable force of the horizontal cable under the above state is:

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