A method for analyzing the damage law of the overall joints of suspension bridges

Abstract

The present invention provides a method for analyzing the damage patterns of the integral nodes of a suspension bridge. This method utilizes a spatial finite element model to determine the most unfavorable position of the integral node of a steel truss and the equivalent stress amplitude of each member, determines the load value used in the fatigue test, verifies the static strength and fatigue strength of the integral node using finite element software, conducts fatigue tests on the steel truss, collects data from the stress measurement points of the integral node, and processes and analyzes the data. While verifying that the fatigue performance of the integral node meets design requirements, a piecewise function is derived to describe the evolution of the damage of the integral node. This function is used to analyze the development patterns of the integral node of a suspension bridge steel truss from the onset of the fatigue cycle to its destruction.

Description

Technical Field

[0001] The present invention belongs to the field of bridge structure safety, and more specifically, relates to a method for analyzing damage laws of overall nodes of a suspension bridge. Background Art

[0002] Integral joint technology was adopted relatively late in my country, and the integral joints currently used in bridges are far from reaching their fatigue lifespan. Therefore, the impact of fatigue loads on integral joints has not been fully reflected. However, with the continuous development of the industry, the fatigue problem of integral joints has become more prominent due to the coupling of various factors.

[0003] Compared to conventional joints, integral joints reduce bolt usage and improve assembly efficiency, making them widely used in long-span bridges. However, the integral joint region is complex, with various chords and web members converging at the integral joint area, where internal forces are transmitted to the gusset plate. Under the cyclic effects of vehicle loads, the stress conditions acting on this structure are particularly complex. Ensuring the normal and safe operation of the integral joint is crucial to the serviceability of the bridge, so research and analysis of the fatigue performance of the integral joint is essential.

[0004] At present, scholars usually use experiments to analyze the fatigue performance of integral nodes. However, most experiments and research analyses are aimed at verifying that the fatigue performance of integral nodes meets their design requirements, and no experimental analysis is conducted to analyze and study the development laws of the entire process from the beginning of the fatigue cycle to destruction. Summary of the Invention

[0005] The purpose of the present invention is to design a fatigue load test for the integral node area in a suspension bridge to ensure that it can work normally. While verifying that the fatigue performance of the integral node meets the bridge design requirements, the test data is summarized and analyzed, and the damage evolution equation of the integral node is derived to obtain the law of the process from the beginning of the fatigue cycle to the destruction of the integral node.

[0006] According to one aspect of the present invention, a method for analyzing the damage pattern of the overall nodes of a suspension bridge is provided, characterized in that it includes the following steps:

[0007] Step 1: Determine the most unfavorable overall node through moving load analysis of the full-bridge finite element model and calculate the 500,000 times equivalent stress amplitude of each member at this node;

[0008] Step 2: Based on similarity theory, a scaled model is designed for the steel truss at the most unfavorable overall node, a beam unit model is established to simulate the loading of the steel truss at the most unfavorable overall node, and the upper and lower limits of fatigue test loading are determined according to the equivalent stress amplitude;

[0009] Step 3: Use finite element analysis software to build a spatial refined model of the scaled model, analyze its static strength and fatigue strength to ensure that its strength meets the requirements;

[0010] Step 4: Design and complete the production of a scaled model, arrange the measuring points required for the test on the model, conduct fatigue load tests according to the designed test process, and record the measuring point data until the specimen breaks and the test is terminated;

[0011] Step 5: Organize the strain data recorded in the load test and analyze whether it is consistent with the test phenomenon. Use the relative change of strain as the damage variable to derive the damage evolution equation of the entire node to obtain the damage evolution law of the entire node.

[0012] Preferably, based on the above scheme, the specific steps of calculating the 500,000 times equivalent stress amplitude of each member of the most unfavorable overall node are: based on the stress frequency spectrum and the number of standard fatigue vehicles, calculating the equivalent stress amplitude of each member, and obtaining the member with the largest 500,000 times equivalent stress amplitude.

[0013] Preferably, based on the above scheme, the finite element analysis software is used to establish a spatial refined model of the scaled model. The specific steps are: using finite element analysis to verify whether the static strength and fatigue strength of the scaled model meet the requirements.

[0014] Preferably, based on the above scheme, in step 4, a fatigue load test is performed on the scaled model, and the specific steps are: using a fatigue testing instrument to load the specimen, and recording the strain data of the measuring points during the fatigue cycle until the specimen breaks and the test is terminated.

[0015] Based on the above scheme, the specific steps of step 5 are as follows: taking the relative change of the strain data recorded in the load test as the damage variable, fitting the piecewise function using the least squares method according to the three-stage process of damage evolution, the damage evolution equation can be determined, and the damage evolution law of the overall node can be obtained.

[0016] Based on the above solution, the damage variable calculation formula is as follows:

[0017]

[0018] Where D is the damage variable; ε is the strain at the cycle number; ε0 is the initial strain; ε u is the strain of the steel truss at fatigue failure.

[0019] Preferably, based on the above scheme, the three-stage process of damage evolution includes a rapid development stage, a stable development stage, and a rapid destruction stage.

[0020] Based on the above solution, the damage pattern in the rapid development stage is preferably:

[0021]

[0022] Where a1 is the constant to be determined under the fatigue test, n is the number of cycles, N is the fatigue life, is the circulation ratio.

[0023] Based on the above solution, the damage law in the stable development stage is preferably:

[0024]

[0025] Where b1, b2, b3, and b4 are the constants to be determined under the fatigue test, n is the number of cycles, and N is the fatigue life. is the circulation ratio.

[0026] Based on the above solution, the damage law in the rapid destruction stage is preferably:

[0027]

[0028] Where c1 and c2 are the constants to be determined under the fatigue test, n is the number of cycles, and N is the fatigue life. The circulation ratio

[0029] The present invention provides a method for analyzing the damage patterns of the integral nodes of a suspension bridge. This method utilizes a spatial finite element model to determine the most unfavorable position of the integral node of a steel truss and the equivalent stress amplitude of each member, determines the load value used in the fatigue test, verifies the static strength and fatigue strength of the integral node using finite element software, conducts fatigue tests on the steel truss, collects data from the stress measurement points of the integral node, and processes and analyzes the data. While verifying that the fatigue performance of the integral node meets design requirements, a piecewise function is derived to describe the evolution of the damage of the integral node. This function is used to analyze the development patterns of the integral node of a suspension bridge steel truss from the onset of the fatigue cycle to its destruction.

[0030] Whether the integral joints can function properly is crucial for the safe commissioning of suspension bridges. Fatigue testing of integral joints can analyze stress data to identify weak spots within the joints, highlighting potential areas of concern. Furthermore, damage evolution equations can be used to assess the safety of suspension bridges after their commissioning, providing a reference for their structural safety performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a schematic diagram of a full-bridge finite element model of the present invention;

[0032] Figure 2This is a schematic diagram of the static strength analysis of the refined model of the present invention;

[0033] Figure 3 This is a schematic diagram of regional fatigue strength analysis of the high-strength bolt of the present invention;

[0034] Figure 4 This is a schematic diagram of fatigue strength analysis of the non-high-strength bolt area of ​​the present invention;

[0035] Figure 5 This is a flow chart of the method for analyzing the damage law of the overall nodes of a suspension bridge according to the present invention. DETAILED DESCRIPTION

[0036] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0037] See also Figure 5 As shown, the present invention provides a method for analyzing the damage law of the overall node of a suspension bridge, comprising the following steps:

[0038] S1, using the finite element full bridge model, such as Figure 1 As shown, determine the most unfavorable node and the 500,000 times equivalent stress amplitude of each member at this node:

[0039] S11. By establishing a finite element model of the entire bridge and performing moving load analysis according to the British BS5400 standard, the typical nodes with the largest stress amplitude of each member are obtained, as shown in Table 1 below.

[0040] Table 1 Typical overall node stress amplitude (unit: MPa)

[0041]

[0042] After comprehensive consideration of the stress amplitudes of the above nodes, it can be concluded that node 881 is the most unfavorable node under fatigue.

[0043] S12. Calculate the axial stress influence line of each member at the most unfavorable node when loading each lane using the full-bridge finite element model. Load the slow lane and adjacent lanes with a standard fatigue vehicle according to the influence line to obtain the stress history of each member. Then, use the rainflow counting method to determine the amplitude and number of cycles, thereby obtaining the stress frequency spectrum.

[0044] S13. According to traffic volume forecast, the average daily traffic volume of the bridge in 100 years is 56,129 veh·d. -1Taking all factors into consideration, we take 5% of the total traffic volume as the standard fatigue vehicle number. For a six-lane, two-way road, the ratio of slow lane to adjacent lane traffic volume is 2:1.5. This yields a 100-year standard fatigue vehicle traffic volume of 29.3142 million slow lanes and 21.986 million adjacent lanes.

[0045] S14. Based on the stress frequency spectrum and the number of standard fatigue vehicles, the British BS5400 standard and Miner criterion are adopted to calculate the 500,000 times equivalent stress amplitude of the rod by formula (1):

[0046]

[0047] Where Δσ is the equivalent stress amplitude; Δσ i is the stress amplitude under the action of a standard fatigue car; n0 is the equivalent cycle number, which is 500,000 times; n i is the number of fatigue vehicles passing through each lane; K F is the correction coefficient for the multi-vehicle effect; m is the negative inverse of the SN curve efficiency.

[0048] After calculating the equivalent stress amplitude of each member, it was found that the equivalent stress amplitude of the left diagonal web at the most unfavorable node was the largest, which was 140.02 MPa.

[0049] S2. Use the obtained equivalent stress amplitude to determine the upper and lower limits of fatigue load:

[0050] S21. Based on similarity theory, a 1:4 scale model was designed for the steel truss segment at the most unfavorable node, using the same materials as the bridge. Finite element analysis software was then used to simulate fatigue loading by applying a load at the midpoint of the top chord using the scaled steel truss beam model and simply supported boundary conditions. The results showed that when the load reached 450 kN, the maximum axial stress in the diagonal web was 143.7 MPa. Therefore, the upper limit of the fatigue test load was set at 500 kN, and the lower limit was set at 50 kN.

[0051] S3. For the upper and lower limits of fatigue loading, perform refined finite element static strength and fatigue strength analysis on the most unfavorable overall node:

[0052] S31. For the fatigue load upper limit of 500kN, perform static strength analysis on the scaled model of the most unfavorable node, such as Figure 3As shown in the figure. Based on the Saint-Venant principle, finite element software was used to establish a local model of the overall node. Each member was cut sufficiently far from the overall node. The internal forces of each section under a 500kN load in the steel truss beam element model were used as force boundary conditions, and a simply supported constraint was used as a displacement boundary condition at the cut section of the lower chord. After defining the contact points at each location, the model was solved, ignoring stress singularities and stress concentrations. The maximum Von-Mises stress of the model was less than the yield strength of 345MPa, thus meeting the static strength requirements.

[0053] S32. For a fatigue load amplitude of 450kN, fatigue strength analysis was performed on the scaled model of the most unfavorable node. Combining the structural details of the "Code for Design of Highway Steel Bridges" (JTG D64-2015), fatigue assessment was performed on the high-strength bolt connection area of ​​the diagonal web. The fatigue detail category of the diagonal web is 110, and its fatigue strength after 500,000 cycles is 174.61MPa. The calculated axial stress cloud of the diagonal web shows a maximum axial stress of 153.31MPa, which is less than 174.61MPa. Figure 3 As shown. In the non-high-strength bolt connection area, the SN curve of Q345qD is used for fatigue assessment. The SN curve with a guarantee rate of 99% is lg(N)=27.650-9.543lg(S). Its 500,000 times fatigue strength is 199.63MPa. The stress cloud diagram of the bolt area is calculated as follows: Figure 4 As shown in the figure, judging by the color of the stress cloud map, the maximum Von-Mises stress is less than 199.63 MPa, so the fatigue strength of the overall node area meets the design requirements.

[0054] S4. Use the determined upper and lower limits of fatigue loading and conduct fatigue load tests according to the designed test process:

[0055] S41. Design and complete the fatigue test model according to a 1:4 scale ratio. Based on the stress cloud map obtained in the previous step, arrange a total of 28 measuring points at the overall nodes, arrange 25 strain gauges symmetrically along the axial direction of each rod, and arrange 3 strain rosettes at the chamfers.

[0056] S42. The fatigue test model adopts the boundary conditions of simple supports at both ends, and uses the MTS electro-hydraulic servo actuator to perform vertical downward single-point loading at the top midpoint of the upper chord of the integral node. Pre-loading should be carried out before loading to eliminate the gaps between the components and ensure that all measuring points and instruments can operate normally. The upper and lower limits of fatigue loading are 500kN and 50kN respectively, which are obtained in the previous steps. During the fatigue test, the machine is shut down after every 50,000 cycles and static loading is performed three times. Each static loading is loaded step by step from 0kN to 500kN and then unloaded step by step to 0kN. Each load level is set to 50kN. After each equal reading is stable, the data of each measuring point is recorded.

[0057] S43. Observation of each member during the fatigue test revealed six cracks: four on the right diagonal member, one on the left diagonal member, and one on the vertical member. The first crack appeared at the second row of bolts in the upper flange splice of the right diagonal member at 245,700 cycles. When the fatigue cycle count reached 423,000, the right diagonal member suddenly broke, with full-section transverse cracks appearing at the first row of bolt holes. The fatigue test was terminated.

[0058] S5. Organize and analyze the strain data of the measuring points obtained from the test to verify whether they are consistent with the test phenomena. Then use the strain data of the measuring points near the damage location to determine the damage variables, derive the damage evolution equation, and obtain the overall node damage evolution law:

[0059] S51. When the load level is 500kN, the upper limit of the fatigue test, the stress of each measuring point at the beginning of the cycle is compared with the finite element analysis results. The error between the two is within an acceptable range, indicating that the finite element simulation is relatively accurate and the test results are credible.

[0060] S52. When the load level is the fatigue upper limit of 500kN, the stress changes of some measuring points with the number of cycles are summarized and graphed. It is found that the stresses of the measuring points on the vertical webs are all negative. Fatigue damage does not need to be considered for compressive members. No cracks occur in the vertical webs, which is consistent with the test phenomenon. The stress at the upper end of the measuring point at the mid-span of the lower chord gradually decreases, while the stress at the lower end of the mid-span gradually increases, which is consistent with the stress condition of the lower chord. No cracks occur in the lower chord, which is consistent with the test phenomenon. The stress difference of the measuring points on the diagonal web is not large at the beginning of the test. As the number of cycles increases, the stress difference tends to increase. The stress of the measuring points on the left diagonal web gradually decreases, while the stress of the measuring points on the right diagonal web gradually increases. Therefore, the fatigue damage degree of the right diagonal web is greater than that of the left diagonal web, which is consistent with the result that the right diagonal web suffers fatigue fracture.

[0061] S53. In order to analyze the damage evolution law of the overall node, the stress trend of the measuring points near the failure position with the increase of static loading level was plotted into a chart for analysis. It was found that the stress of the P1 measuring point gradually decreased with the increase of the number of cycles, and the decreasing speed changed from fast to slow. The stress of the P1' measuring point dropped sharply at 100,000-150,000 cycles, reflecting that the stress of each point inside the right diagonal web was redistributed at this time. It increased in the opposite direction at 150,000-400,000 cycles at a relatively stable speed. The final stress was greater than the initial stress, and it finally broke, and the test was terminated.

[0062] S54. Using the relative change in strain as the damage variable, the damage evolution equation is derived. Since the strain at fatigue failure cannot be measured, the damage degree at the stable development stage of damage can be taken as 1 / 2 of the damage degree at failure. Plotting the damage variable as the cycle ratio n / N changes in the graph, it can be found that the damage evolution of the overall node has a very obvious three-stage change. Using the least squares method to fit the above three stages, the damage evolution equation of the overall node of the steel truss under this fatigue test can be obtained, as shown in Equation (2):

[0063]

[0064] Finally, the method of this application is only a preferred embodiment and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for analyzing the damage law of the overall nodes of a suspension bridge, characterized in that: The steps include: Step 1: Determine the most unfavorable overall node through moving load analysis of the full-bridge finite element model and calculate the 500,000 times equivalent stress amplitude of each member at that node; Step 2: Based on similarity theory, a scaled model is designed for the steel truss at the most unfavorable overall node, a beam unit model is established to simulate the loading of the steel truss at the most unfavorable overall node, and the upper and lower limits of fatigue test loading are determined according to the equivalent stress amplitude; Step 3: Use finite element analysis software to build a spatial refined model of the scaled model, analyze its static strength and fatigue strength to ensure that its strength meets the requirements; Step 4: Design and complete the production of a scaled model, arrange the measuring points required for the test on the model, conduct fatigue load tests according to the designed test process, and record the measuring point data until the specimen breaks and the test is terminated; Step 5: Organize the strain data recorded by the load test and analyze whether it is consistent with the test phenomenon. Use the relative change of strain as the damage variable to derive the damage evolution equation of the entire node to obtain the damage evolution law of the entire node. The specific steps of step 5 are as follows: taking the relative change of the strain data recorded in the load test as the damage variable, fitting the piecewise function using the least squares method according to the three-stage process of damage evolution, determining the damage evolution equation, and obtaining the damage evolution law of the entire node; The damage pattern in the rapid development stage is: Formula (2); Where a1 is the constant to be determined under the fatigue test, is the number of cycles, is the fatigue life, is the circulation ratio; The damage pattern in the stable development stage is: Formula (3); Where b1, b2, b 3、 b4 is the undetermined constant under the fatigue test, is the number of cycles, is the fatigue life, is the circulation ratio; The damage law in the rapid destruction stage is: Formula (4); Where c1 and c2 are the constants to be determined under the fatigue test. is the number of cycles, is the fatigue life, is the circulation ratio.

2. The method for analyzing the damage law of the overall node of a suspension bridge according to claim 1, characterized in that: The specific steps of calculating the 500,000 times equivalent stress amplitude of each member of the most unfavorable overall node are: based on the stress frequency spectrum and the number of standard fatigue vehicles, calculating the equivalent stress amplitude of each member, and obtaining the member with the largest 500,000 times equivalent stress amplitude.

3. The method for analyzing the damage law of the overall node of a suspension bridge according to claim 1, characterized in that: The method of using finite element analysis software to establish a spatial refined model for the scaled model specifically comprises the steps of using finite element analysis to verify whether the static strength and fatigue strength of the scaled model meet the requirements.

4. The method for analyzing the damage law of the overall node of a suspension bridge according to claim 1, characterized in that: In step 4, a fatigue load test is performed on the scaled model. Specifically, a fatigue test instrument is used to load the specimen, and strain data of the measuring points during the fatigue cycle are recorded until the specimen breaks and the test is terminated.

5. The method for analyzing the damage law of the overall node of a suspension bridge according to claim 1, characterized in that: The damage variable calculation formula is: Formula (1); Where D is the damage variable; is the strain under the cycle number; is the initial strain; is the strain of the steel truss at fatigue failure.

6. The method for analyzing the damage law of the overall node of a suspension bridge according to claim 1, characterized in that: The three-stage process of damage evolution includes a rapid development stage, a stable development stage, and a rapid destruction stage.

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