Method for evaluating dynamic response of large-span suspension bridge under combined action of wind and shock

Abstract

The invention provides a method for evaluating the dynamic response of a large-span suspension bridge under the combined action of wind and shock, and particularly relates to the technical field of bridge engineering structure safety and disaster prevention and reduction. The method comprises the following steps: S1, establishing a bridge finite element model by using ANSYS software; s2, performing modal analysis on the finite element model to determine natural vibration frequency; s3, determining selection and reading of seismic waves; s4, calculating a rotation matrix; s5, simulating a fluctuating wind speed spectrum by using the Simiu power spectrum and determining the fitting degree of the fluctuating wind speed spectrum and the target spectrum; s6, applying a load to the finite element model established in the step S1; s7, calculating a dynamic response value under the combined action of the earthquake and the wind load; and S8, performing drawing analysis on the internal force and the displacement response value by utilizing ORIGIN software. According to the method, ANSYS software is used for carrying out load dynamic response analysis, the effect of earthquake and wind load on the combined action of the bridge is comprehensively and systematically investigated, accurate assessment of risk disasters in the construction stage and the bridge forming stage under the action of multiple disasters is achieved, and the safety and reliability of the bridge structure are ensured.

Description

Technical Field

[0001] The patent of this invention relates to the field of bridge engineering structural safety and disaster prevention and mitigation technology, and specifically to a method for evaluating the dynamic response of a large-span suspension bridge under the combined action of wind and earthquake. Background Art

[0002] The widespread use of long-span bridges has become a significant trend in modern bridge engineering. These bridges typically possess structural characteristics of large spans, high flexibility, and low damping, making them more sensitive to natural disasters such as wind and earthquakes. Earthquakes are often accompanied by strong winds, and the two are closely and complexly linked. In actual bridge loading, wind loads and seismic forces interact, and their combined effects can cause even more severe damage to bridge structures.

[0003] In the past, the dynamic response analysis of bridges under wind loads and earthquakes was usually conducted separately. Although a relatively mature assessment method and system has been formed for the dynamic response analysis of bridges under single disasters, this separate analysis method has theoretical flaws because it ignores the objective joint action relationship between wind disasters and earthquakes. It cannot truly restore the damage process of bridges under multiple disasters and it is difficult to accurately assess the actual damage to the bridges.

[0004] In recent years, research on the safety of structures under the combined action of multiple disasters has received increasing attention. The analysis of the dynamic response of bridges under the combined action of multiple disasters can more accurately restore the actual damage process when they are actually affected by disasters, and is also more consistent with the actual situation in theory.

[0005] The existing bridge dynamic response analysis schemes have the following problems: 1. They focus too much on the dynamic response analysis under a single load. When faced with the combined effects of multiple disasters such as earthquakes and wind loads, they cannot comprehensively and reasonably simulate the actual disaster situation of the bridge, making it difficult to accurately assess the actual damage status of the bridge; 2. In the dynamic response analysis of bridges under the combined effects of earthquakes and wind loads, the influence of load directionality is not systematically considered, resulting in limitations in the safety assessment of bridge structures; 3. They mainly focus on the operation stage after the bridge is built, and there is insufficient research on the stability and safety of bridge structures under the effects of multiple disasters during the construction process, resulting in a complete safety assessment. Summary of the Invention

[0006] To overcome the above-mentioned deficiencies of the prior art, the present invention provides a method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake. The specific technical solution is as follows:

[0007] A method for evaluating the dynamic response of a long-span suspension bridge under combined wind and earthquake action comprises the following steps:

[0008] S1. Use ANSYS software to build a finite element model of the bridge;

[0009] S2. Perform modal analysis on the finite element model to determine the natural frequency and vibration period;

[0010] S3. Determine the selection and reading of seismic waves;

[0011] S4. Calculate the rotation matrix;

[0012] S5. Use Simiu power spectrum to simulate the fluctuating wind speed spectrum and determine the degree of fit between the fluctuating wind speed spectrum and the target spectrum;

[0013] S6. Apply load to the finite element model established in S1;

[0014] S7. Calculate the dynamic response under the combined action of earthquake and wind loads;

[0015] S8. Use ORIGIN software to plot and analyze the internal force and displacement response values.

[0016] Preferably, the step S1 of establishing a finite element model of a bridge using ANSYS software specifically includes the following sub-steps:

[0017] S1.1 Obtain architectural drawings of the actual structure of the 3D suspension bridge to be evaluated and use ANSYS finite element software to model the bridge during the construction phase. Beam4 elements are used to simulate the stiffening beams and pylons, which are the main load-bearing structures of the 3D suspension bridge to be evaluated. Link10 elements are used to simulate the main cables and suspenders.

[0018] S1.2 Based on the generated finite element model of the bridge at the construction stage, the second-stage dead load is applied to the stiffening beam using ANSYS finite element software, including the bridge deck pavement and ancillary facilities, to obtain the finite element model of the bridge at the completion stage. The second-stage dead load application is simulated using the MASS21 quality element type.

[0019] S1.3 sets boundary conditions for the base of the pylons, the ends of the main cables, the main cables and the tops of the pylons, and between the stiffening beams and the pylons, i.e., degree-of-freedom constraints. The base of the pylons and the ends of the main cables are fully consolidated; the main cables and the tops of the pylons are rigidly connected; and the stiffening beams and pylons are node-coupled.

[0020] S1.4 After completing the modeling and boundary condition setting, static analysis tests are performed on the finite element model of the bridge in the construction stage and the finite element model of the bridge in the completion stage:

[0021] If the maximum main cable tension response value of the bridge is ≤250,000 kN and the maximum displacement response value is ≤10 cm, the static analysis test complies with the specifications, which means that the constructed finite element model of the bridge during the construction phase and the finite element model of the bridge during the completion phase are accurate and reliable;

[0022] If the static analysis test does not meet the requirements, the boundary conditions are corrected by continuously executing the command flow until the static analysis test meets the requirements.

[0023] Preferably, the modal analysis of the finite element model in S2 to determine the natural frequency and vibration period is specifically:

[0024] Based on the influence of boundary conditions and element types determined in S1 on the analysis results, the Block Lanczos method was used to perform modal analysis on the finite element models of the bridge during the construction and completion stages. The natural frequencies and mode shapes corresponding to the natural frequencies of the three-dimensional suspension bridge structure to be evaluated were obtained during the construction and completion stages, respectively, and the vibration period was calculated.

[0025] Preferably, the step S3 of determining the selection and reading of seismic waves specifically includes the following sub-steps:

[0026] S3.1 Based on the basic principles of the three-dimensional suspension bridge structure type and site type to be assessed, select seismic waves in the X-axis, Y-axis, and Z-axis directions that match the basic ground motion peak acceleration data and the characteristic period of the standard spectrum in the area where the three-dimensional suspension bridge to be assessed is located;

[0027] S3.2 defines three arrays for storing seismic waves in the X-axis, Y-axis, and Z-axis directions. The acceleration data of the seismic waves in the X-axis, Y-axis, and Z-axis directions in the original coordinate system are read one by one into the arrays in the corresponding directions using the ANSYS software data reading command.

[0028] Preferably, the calculation of the rotation matrix in S4 specifically includes the following sub-steps:

[0029] S4.1 sets the actual incident direction of the seismic wave determined in S3.1 and determines the rotation angle θ around the X-axis, Y-axis, and Z-axis. x ,θ y ,θ z And convert the rotation angle into radians uniformly;

[0030] S4.2 Rotate the matrix R around the X axis in the order of X axis, Y axis, and Z axis. x (θ x ), the matrix R of rotation around the Y axis y (θ y ) and the matrix R for rotation around the Z axis z (θ z) and multiply them to get the total rotation matrix formula:

[0031] R=R x (θ x )·R y (θ y )·R z (θ z )(1);

[0032] After matrix multiplication, we can get:

[0033]

[0034] S4.3 Convert the rotation angle in radians according to S4.1 and calculate the corresponding trigonometric function value cosθ in equation (2) in 4.2 x 、sinθ x 、cosθ y 、sinθ y 、cosθ z 、sinθ z ;

[0035] S4.4 calculates the required seismic wave rotation matrix for any incident direction of the X-axis, Y-axis, and Z-axis based on equation (2) in S4.2 as shown below:

[0036]

[0037] Substitute the trigonometric function values ​​obtained in S4.3 into equation (3) to calculate the values ​​of each element in the seismic wave rotation matrix for any incident direction;

[0038] The acceleration matrix of the original seismic wave in the global coordinate system is defined as:

[0039]

[0040] Among them, a x 、a y 、a z are the acceleration data of the original seismic wave along the X-axis, Y-axis, and Z-axis in the global coordinate system;

[0041] After the rotation matrix transformation, the final acceleration matrix of the seismic wave in the local coordinate system is:

[0042]

[0043] Among them, the acceleration matrix coefficient in the local coordinate system is the element r in the rotation matrix of formula (3): mn , r mn is the value of the element in the mth row and nth column of the rotation matrix of formula (3); m=1,2,3; n=1,2,3; a′ x, a′ y , a′ z They are respectively the acceleration data of the final seismic wave along the X-axis, Y-axis, and Z-axis in the local coordinate system.

[0044] Also preferably, S5 uses Simiu power spectrum to simulate the fluctuating wind speed spectrum and determines the degree of fit between the fluctuating wind speed spectrum and the target spectrum, specifically including the following sub-steps:

[0045] S5.1 Obtain the surface roughness coefficient of the area based on the topographical features of the site of the three-dimensional suspension bridge to be evaluated, query the average wind speed of the bridge site, and use the average wind speed as the basic parameter;

[0046] S5.2 simulates the fluctuating wind speed using the autoregressive model method based on the average wind speed and the surface roughness coefficient;

[0047] S5.3 Select a target spectrum and verify the consistency between the target spectrum and its corresponding fluctuating wind spectrum, and select the fluctuating wind spectrum with the highest consistency with the target spectrum;

[0048] S5.4 superimposes the average wind speed obtained in S5.1 and the fluctuating wind speed simulated in S5.2 to obtain the time-varying natural wind speed time history data, which is used as the wind load subsequently applied to the finite element model.

[0049] Further preferably, the step of applying a load to the finite element model established in step S1 in step S6 specifically includes:

[0050] Using the ACEL command of ANSYS finite element software, the seismic wave working condition is set according to the rotation angle, and the wind load working condition is set according to the wind attack angle. The seismic wave acceleration data a′ obtained in S4.5 formula (5) is converted to x , a′ y , a′ z The wind loads obtained in S5.4 are applied to the finite element model of the bridge in the construction stage and the finite element model of the bridge in the completion stage, respectively.

[0051] Further preferably, the calculation of the dynamic response value under the combined action of earthquake and wind loads in S7 specifically includes the following sub-steps:

[0052] S7.1 uses transient analysis as the analysis type and determines the time step based on the frequency characteristics of seismic waves, the fluctuating wind characteristics, and the vibration period of the bridge structure;

[0053] S7.2 Based on the natural frequencies obtained in S3, calculate the Rayleigh damping parameters α and β and use ANSYS software to proportionally distribute the damping ratio to the mass term and the stiffness term;

[0054] S7.3 takes the time period for the combined action of earthquake and wind loads as the total solution time;

[0055] S7.4 Based on the parameters obtained in S7.1-S7.3, use ANSYS software to determine the displacement and internal force response values ​​of the three-dimensional suspension bridge structure to be evaluated under the combined action of earthquake and wind loads.

[0056] More preferably, the drawing analysis of the internal force and displacement response values ​​using ORIGIN software in S8 specifically includes the following sub-steps:

[0057] S8.1 Import the displacement and internal force response data obtained in S7.4 into the ORIGIN software and plot the horizontal tower top displacement diagrams for the three-dimensional suspension bridge to be evaluated during the construction and completion stages.

[0058] S8.2 Compare the maximum horizontal tower top displacement and safety factor during the construction and completion phases with the allowable values ​​in the code:

[0059] If the maximum horizontal tower top displacement is less than tower height / 100 and the safety factor is greater than 2.5, the bridge structure of the three-dimensional suspension bridge to be evaluated meets the requirements and does not require reinforcement; otherwise, the bridge structure of the three-dimensional suspension bridge to be evaluated does not meet the requirements, and the superstructure of the bridge tower of the three-dimensional suspension bridge to be evaluated needs to be inspected or reinforced.

[0060] The beneficial effects of the present invention are:

[0061] 1. This invention uses multi-software collaborative precision analysis to comprehensively consider the combined impact of earthquakes and wind loads on bridge structures. This significantly improves the accuracy and reliability of bridge dynamic response analysis under the combined effects of earthquakes and wind loads. It can provide a scientific basis for bridge safety assessment, help improve bridge disaster resistance, and ensure safe bridge operation.

[0062] 2. The present invention dynamically transforms seismic waves from the global coordinate system to the local coordinate system of the structure through a rotation matrix before applying loads. Wind loads are applied by changing the wind attack angle, achieving precise directional distribution of seismic waves and wind loads.

[0063] 3. The present invention not only analyzes the bridge operation phase, but also analyzes the dynamic response under the combined action of earthquake and wind loads during the construction phase. It can effectively deal with sudden earthquakes and wind disasters during construction, and reasonably conduct risk assessment and prevention. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The drawings constituting the description of the present invention are used to provide further understanding of the present application and do not constitute an improper limitation to the present application.

[0065] Figure 1 Provides a main flow chart of the evaluation method of the present invention;

[0066] Figure 2 is a schematic diagram of a bridge model of the present invention;

[0067] FIG3( a ) is a bridge model of the present invention during the construction phase;

[0068] FIG3( b ) is a bridge model of the present invention at the completion stage;

[0069] Figure 4 The earthquake record response spectrum curve of the present invention;

[0070] Figure 5 The acceleration time history curve of the earthquake motion recording of the present invention;

[0071] Figure 6 The pulsating wind speed time history curve of the present invention;

[0072] Figure 7 This is a comparison diagram of the simulated fluctuating wind speed spectrum and the target spectrum at the stiffening beam position of the present invention;

[0073] Figure 8 A comparison diagram of the simulated fluctuating wind speed spectrum and the target spectrum at the bridge tower position of the present invention;

[0074] Figure 9 is the natural wind speed time history curve of the present invention;

[0075] Figure 10 This is a schematic diagram of the bridge force under the combined action of earthquake and wind loads of the present invention;

[0076] Figure 11 is a horizontal tower top displacement diagram of the bridge during the construction phase of the present invention;

[0077] Figure 12 This is a horizontal tower top displacement diagram of the bridge in the completion stage of the present invention. DETAILED DESCRIPTION

[0078] The specific implementation of the method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake provided by the present invention is further described in conjunction with the drawings and examples.

[0079] like Figure 1 As shown, a method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake is characterized by comprising the following steps:

[0080] S1. Figure 2 As shown in Figure 3, the finite element model of the bridge is established using ANSYS software, which includes the following sub-steps:

[0081] S1.1 Obtain architectural drawings of the actual structure of the 3D suspension bridge to be evaluated and use ANSYS finite element software to model the bridge during the construction phase. Beam4 elements are used to simulate the stiffening beams and pylons, which are the main load-bearing structures of the 3D suspension bridge to be evaluated. Link10 elements are used to simulate the main cables and suspenders.

[0082] S1.2 Based on the generated finite element model of the bridge at the construction stage, the second-stage dead load is applied to the stiffening beam using ANSYS finite element software, including the bridge deck pavement and ancillary facilities, to obtain the finite element model of the bridge at the completion stage. The second-stage dead load application is simulated using the MASS21 quality element type.

[0083] S1.3 Set boundary conditions for the base of the pylon, the ends of the main cables, the main cables and the top of the pylons, and between the stiffening beams and the pylons, i.e., degree-of-freedom constraints, as shown in Table 1 below. The base of the pylons and the ends of the main cables are fully consolidated; the main cables and the top of the pylons are rigidly connected; and the stiffening beams and pylons are node-coupled.

[0084] Table 1. Freedom constraints of bridge model

[0085]

[0086] S1.4 After completing the modeling and boundary condition setting, static analysis tests are performed on the finite element model of the bridge in the construction stage and the finite element model of the bridge in the completion stage:

[0087] If the maximum main cable tension response value of the bridge is ≤250,000 kN and the maximum displacement response value is ≤10 cm, the static analysis test complies with the specifications, which means that the constructed finite element model of the bridge during the construction phase and the finite element model of the bridge during the completion phase are accurate and reliable;

[0088] If the static analysis test does not meet the requirements, the boundary conditions are corrected by continuously executing the command flow until the static analysis test meets the requirements.

[0089] S2. Perform modal analysis on the finite element model to determine the natural frequency and vibration period. Specifically:

[0090] Based on the influence of the boundary conditions and element types determined in S1 on the analysis results, the Block Lanczos method was used to perform modal analysis on the finite element models of the bridge in the construction stage and the completion stage. The natural frequencies of the three-dimensional suspension bridge structure to be evaluated in the construction stage and the completion stage were obtained (in this embodiment, the first 20 orders were taken, see Table 2 below for details), the mode shapes corresponding to the natural frequencies, and the vibration period were calculated.

[0091] Table 2. The first 20 natural vibration frequencies of the bridge during the construction and completion stages

[0092]

[0093]

[0094] S3. Determine the selection and reading of seismic waves, specifically including the following sub-steps:

[0095] S3.1 Based on the basic principles of the three-dimensional suspension bridge structure type and site type to be assessed, select seismic waves in the X-axis, Y-axis, and Z-axis directions that match the basic ground motion peak acceleration data (see Table 3 below) and the characteristic period of the standard spectrum in the area where the three-dimensional suspension bridge to be assessed is located;

[0096] Table 3. Original seismic wave acceleration data in the X, Y, and Z directions

[0097]

[0098]

[0099] Specific earthquake motion information is shown in Table 4 below:

[0100] Table 4. Earthquake information

[0101]

[0102] S3.2 defines three arrays for storing seismic waves in the X-axis, Y-axis, and Z-axis directions. Using the ANSYS software data read command, the acceleration data of the seismic waves in the X-axis, Y-axis, and Z-axis directions in the original coordinate system are read one by one into the arrays in the corresponding directions.

[0103] The earthquake record response spectrum curve and acceleration time history curve selected in this embodiment are as follows: Figure 4-Figure 5 shown.

[0104] S4. Calculate the rotation matrix, specifically including the following sub-steps:

[0105] S4.1 sets the actual incident direction of the seismic wave determined in S3.1 and determines the rotation angle θ around the X-axis, Y-axis, and Z-axis. x ,θ y ,θ z And convert the rotation angle into radians uniformly;

[0106] S4.2 Rotate the matrix R around the X axis in the order of X axis, Y axis, and Z axis. x (θ x ), the matrix R of rotation around the Y axis y (θ y ) and the matrix R for rotation around the Z axis z (θz ) and multiply them to get the total rotation matrix formula:

[0107] R=R x (θ x )·R y (θ y )·R z (θ z )(1);

[0108] After matrix multiplication, we can get:

[0109]

[0110] S4.3 Convert the rotation angle in radians according to S4.1 and calculate the corresponding trigonometric function value cosθ in equation (2) in 4.2 x 、sinθ x 、cosθ y 、sinθ y 、cosθ z 、sinθ z ;

[0111] S4.4 calculates the required seismic wave rotation matrix for any incident direction of the X-axis, Y-axis, and Z-axis based on equation (2) in S4.2 as shown below:

[0112]

[0113] Substitute the trigonometric function values ​​obtained in S4.3 into equation (3) to calculate the values ​​of each element in the seismic wave rotation matrix for any incident direction;

[0114] The acceleration matrix of the original seismic wave in the global coordinate system is defined as:

[0115]

[0116] Among them, a x 、a y 、a z are the acceleration data of the original seismic wave along the X-axis, Y-axis, and Z-axis in the global coordinate system;

[0117] After the rotation matrix transformation, the final acceleration matrix of the seismic wave in the local coordinate system is:

[0118]

[0119] Among them, the acceleration matrix coefficient in the local coordinate system is the element r in the rotation matrix of formula (3): mn , r mn is the value of the element in the mth row and nth column of the rotation matrix of formula (3); m=1,2,3; n=1,2,3; a′x , a′ y , a′ z They are respectively the acceleration data of the final seismic wave along the X-axis, Y-axis, and Z-axis in the local coordinate system.

[0120] S5. Use the Simiu power spectrum to simulate the fluctuating wind speed spectrum and determine the degree of fit between the fluctuating wind speed spectrum and the target spectrum, specifically including the following sub-steps:

[0121] S5.1 Obtain the surface roughness coefficient of the area based on the topographical features of the site of the three-dimensional suspension bridge to be evaluated, query the average wind speed of the bridge site, and use the average wind speed as the basic parameter. See Table 5 below for details:

[0122] Table 5. Average wind speed data at the stiffening beam and bridge tower locations

[0123] Location Average wind speed / (m / s) Stiffening beam 35.7385945397984 Bridge Tower 40.5818514632546

[0124] S5.2 Based on the average wind speed and the surface roughness coefficient, the autoregressive model method is used to simulate the fluctuating wind speed at the stiffening beam and bridge tower. The obtained fluctuating wind speed time history curve is as follows: Figure 6 The pulsating wind speed time history data is shown in Table 6 below:

[0125] Table 6. Fluctuating wind speed time history data at the stiffening beam and bridge tower locations

[0126]

[0127]

[0128] S5.3 Select the target spectrum and verify the consistency between the target spectrum and its corresponding pulsating wind spectrum. Select the pulsating wind spectrum with the highest consistency with the target spectrum (such as Figure 7-Figure 8 shown);

[0129] The selected target spectrum data are detailed in Table 7 below:

[0130] Table 7. Target spectrum data at the stiffening beam and bridge tower positions

[0131]

[0132]

[0133] The fluctuating wind speed data at the stiffening beam and bridge tower locations are shown in Table 8 below:

[0134] Table 8. Fluctuating wind spectrum data at the stiffening beam and bridge tower locations

[0135] Frequency / (HZ) Fluctuating wind spectrum of stiffening beam / (W / Hz) Pylon pulsating wind spectrum / (W / Hz) 0 108.9971258 75.52181406 0.048828125 154.3927491 118.4459218 0.09765625 64.7244971 60.30238378 0.146484375 32.14962316 24.15558201 0.1953125 23.00838832 9.684021982 0.244140625 18.3717797 4.336597013 0.29296875 15.69298922 2.220177115 0.341796875 10.97083479 1.676064205 0.390625 4.825650256 2.301742032 0.439453125 2.681208075 2.034502199 0.48828125 3.386578041 1.293871637 0.537109375 3.596306487 1.237660351 0.5859375 2.755763024 1.566368999 0.634765625 2.008750296 1.511430365 0.68359375 1.61566074 1.05495838 0.732421875 1.706257229 0.766919515 0.78125 1.953340521 0.477084923 0.830078125 1.733822246 0.311290353 0.87890625 1.737696118 0.557580257 0.927734375 1.685306023 0.709844079

[0136] S5.4 superimposes the average wind speed obtained in S5.1 and the fluctuating wind speed simulated in S5.2 to obtain the time-varying natural wind speed time history data (see Table 9 below for details), which is used as the wind load subsequently applied to the finite element model. Figure 9 As shown;

[0137] Table 9. Time history data of natural wind speed at the locations of stiffening beams and bridge towers

[0138]

[0139]

[0140] S6. Apply loads to the finite element model established in S1, including:

[0141] Using the ACEL command of ANSYS finite element software, the seismic wave working condition is set according to the rotation angle, and the wind load working condition is set according to the wind attack angle. The seismic wave acceleration data a′ obtained in S4.5 formula (5) is converted to x , a′ y , a′ z The wind loads obtained in S5.4 are applied to the finite element model of the bridge in the construction stage and the finite element model of the bridge in the completion stage respectively (the schematic diagram of the bridge under the combined action of earthquake and wind loads is shown in Figure 2). Figure 10 The load conditions are shown in Table 10 below:

[0142] Table 10. Applied load conditions

[0143]

[0144] S7. Calculate the dynamic response under the combined action of earthquake and wind loads, including the following sub-steps:

[0145] S7.1 uses transient analysis as the analysis type and determines the time step based on the frequency characteristics of seismic waves, the fluctuating wind characteristics, and the vibration period of the bridge structure;

[0146] S7.2 Based on the natural frequencies obtained in S3, calculate the Rayleigh damping parameters α and β and use ANSYS software to proportionally distribute the damping ratio to the mass term and the stiffness term;

[0147] S7.3 takes the time period for the combined action of earthquake and wind loads as the total solution time;

[0148] S7.4 Based on the parameters obtained in S7.1-S7.3, use ANSYS software to determine the displacement and internal force response values ​​of the three-dimensional suspension bridge structure to be evaluated under the combined action of earthquake and wind loads.

[0149] S8. Use ORIGIN software to plot and analyze the internal force and displacement response values. This includes the following sub-steps:

[0150] S8.1 Based on the displacement and internal force response data obtained in S7.4, import them into the ORIGIN software and draw horizontal tower top displacement diagrams for the three-dimensional suspension bridge to be evaluated during the construction and completion stages, as shown in the following example: Figure 11-12 As shown;

[0151] S8.2 Compare the maximum horizontal tower top displacement and safety factor during the construction and completion phases with the allowable values ​​in the code:

[0152] If the maximum horizontal tower top displacement is less than tower height / 100 (in this embodiment, the tower height is 191.1 m) and the safety factor is greater than 2.5, the bridge structure of the three-dimensional suspension bridge to be evaluated meets the requirements and does not require reinforcement. Otherwise, the bridge structure of the three-dimensional suspension bridge to be evaluated does not meet the requirements, and the superstructure of the bridge tower of the three-dimensional suspension bridge to be evaluated needs to be inspected or reinforced.

[0153] Depend on Figure 11-12 It can be seen that the maximum horizontal tower top displacements of the three-dimensional suspension bridge to be evaluated in this embodiment during the construction and completion stages are -0.0690107 m and 0.192747 m, respectively. The main cable axial forces and safety factors are detailed in Table 11 below:

[0154] Table 11. Main cable axial force and safety factor

[0155]

[0156] In summary, the safety factors of the main cables of the three-dimensional suspension bridge to be evaluated in this embodiment are both greater than 2.5 during the construction and completion stages, and the bridge structure meets the requirements and does not require reinforcement.

[0157] In the present invention, the orientation or positional relationship indicated by terms such as "upper", "lower", "bottom", "top", etc. is based on the orientation or positional relationship shown in the accompanying drawings. They are relational words determined only for the convenience of describing the structural relationship of the various parts or elements of the present invention. They do not specifically refer to any part or element in the present invention and cannot be understood as limiting the present invention. Terms such as "connected" and "connect" should be understood in a broad sense, indicating that they can be fixedly connected, integrally connected, or detachably connected; they can be directly connected or indirectly connected through an intermediate medium. For relevant scientific research or technical personnel in this field, the specific meaning of the above terms in the present invention can be determined according to the specific circumstances, and they cannot be understood as limiting the present invention.

[0158] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake, characterized in that: The specific steps include: S1. Use ANSYS software to build a finite element model of the bridge; S2. Perform modal analysis on the finite element model to determine the natural frequency and vibration period; S3. Determine the selection and reading of seismic waves; S4. Calculate the rotation matrix; S5. Use Simiu power spectrum to simulate the fluctuating wind speed spectrum and determine the degree of fit between the fluctuating wind speed spectrum and the target spectrum; S6. Apply load to the finite element model established in S1; S7. Calculate the dynamic response under the combined action of earthquake and wind loads; S8. Use ORIGIN software to plot and analyze the internal force and displacement response values.

2. The method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake according to claim 1 is characterized in that: S1 uses ANSYS software to establish a bridge finite element model, which specifically includes the following sub-steps: S1.1 Obtain architectural drawings of the actual structure of the 3D suspension bridge to be evaluated and use ANSYS finite element software to model the bridge during the construction phase. Beam4 elements are used to simulate the stiffening beams and pylons, which are the main load-bearing structures of the 3D suspension bridge to be evaluated. Link10 elements are used to simulate the main cables and suspenders. S1.2 Based on the generated finite element model of the bridge at the construction stage, the second-stage dead load is applied to the stiffening beam using ANSYS finite element software, including the bridge deck pavement and ancillary facilities, to obtain the finite element model of the bridge at the completion stage. The second-stage dead load application is simulated using the MASS21 quality element type. S1.3 sets boundary conditions for the base of the pylons, the ends of the main cables, the main cables and the tops of the pylons, and between the stiffening beams and the pylons, i.e., degree-of-freedom constraints. The base of the pylons and the ends of the main cables are fully consolidated; the main cables and the tops of the pylons are rigidly connected; and the stiffening beams and pylons are node-coupled. S1.4 After completing the modeling and boundary condition setting, static analysis tests are performed on the finite element model of the bridge in the construction stage and the finite element model of the bridge in the completion stage: If the maximum main cable tension response value of the bridge is ≤250,000 kN and the maximum displacement response value is ≤10 cm, the static analysis test complies with the specifications, which means that the constructed finite element model of the bridge during the construction phase and the finite element model of the bridge during the completion phase are accurate and reliable; If the static analysis test does not meet the requirements, the boundary conditions are corrected by continuously executing the command flow until the static analysis test meets the requirements.

3. The method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake according to claim 2 is characterized in that: S2 performs modal analysis on the finite element model to determine the natural frequency and vibration period as follows: Based on the influence of boundary conditions and element types determined in S1 on the analysis results, the Block Lanczos method was used to perform modal analysis on the finite element models of the bridge during the construction and completion stages. The natural frequencies and mode shapes corresponding to the natural frequencies of the three-dimensional suspension bridge structure to be evaluated were obtained during the construction and completion stages, respectively, and the vibration period was calculated.

4. The method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake according to claim 3 is characterized in that: The step S3 of determining the selection and reading of seismic waves specifically includes the following sub-steps: S3.1 Based on the basic principles of the three-dimensional suspension bridge structure type and site type to be assessed, select seismic waves in the X-axis, Y-axis, and Z-axis directions that match the basic ground motion peak acceleration data and the characteristic period of the standard spectrum in the area where the three-dimensional suspension bridge to be assessed is located; S3.2 defines three arrays for storing seismic waves in the X-axis, Y-axis, and Z-axis directions. ANSYS software data reading commands are used to read the acceleration data of seismic waves in the X-axis, Y-axis, and Z-axis directions in the original coordinate system one by one into the arrays in the corresponding directions.

5. The method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake according to claim 4 is characterized in that: The calculation of the rotation matrix in S4 specifically includes the following sub-steps: S4.1 sets the actual incident direction of the seismic wave determined in S3.1 and determines the rotation angle θ around the X-axis, Y-axis, and Z-axis. x ,θ y ,θ z And convert the rotation angle into radians uniformly; S4.2 Rotate the matrix R around the X axis in the order of X axis, Y axis, and Z axis. x (θ x ), the matrix R of rotation around the Y axis y (θ y ) and the matrix R for rotation around the Z axis z (θ z ) and multiply them to get the total rotation matrix formula: R=R x (i x )·R y (i y )·R z (i z (1); After matrix multiplication, we can get: S4.3 Convert the rotation angle in radians according to S4.1 and calculate the corresponding trigonometric function value cosθ in equation (2) in 4.2 x 、sinθ x 、cosθ y 、sinθ y 、cosθ z 、sinθ z ; S4.4 calculates the required seismic wave rotation matrix for any incident direction of the X-axis, Y-axis, and Z-axis based on equation (2) in S4.2 as shown below: Substitute the trigonometric function values ​​obtained in S4.3 into equation (3) to calculate the values ​​of each element in the seismic wave rotation matrix for any incident direction; The acceleration matrix of the original seismic wave in the global coordinate system is defined as: Among them, a x 、a y 、a z are the acceleration data of the original seismic wave along the X-axis, Y-axis, and Z-axis in the global coordinate system; After the rotation matrix transformation, the final acceleration matrix of the seismic wave in the local coordinate system is: Among them, the acceleration matrix coefficient in the local coordinate system is the element r in the rotation matrix of formula (3): mn , r mn is the value of the element in the mth row and nth column of the rotation matrix of formula (3); m=1,2,3; n=1,2,3; a′ x , a′ y , a′ z They are respectively the acceleration data of the final seismic wave along the X-axis, Y-axis, and Z-axis in the local coordinate system.

6. The method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake according to claim 5 is characterized in that: S5 uses the Simiu power spectrum to simulate the fluctuating wind speed spectrum and determines the degree of fit between the fluctuating wind speed spectrum and the target spectrum. It specifically includes the following sub-steps: S5.1 Obtain the surface roughness coefficient of the area based on the topographical features of the site of the three-dimensional suspension bridge to be evaluated, query the average wind speed of the bridge site, and use the average wind speed as the basic parameter; S5.2 simulates the fluctuating wind speed using the autoregressive model method based on the average wind speed and the surface roughness coefficient; S5.3 Select a target spectrum and verify the consistency between the target spectrum and its corresponding fluctuating wind spectrum, and select the fluctuating wind spectrum with the highest consistency with the target spectrum; S5.4 superimposes the average wind speed obtained in S5.1 and the fluctuating wind speed simulated in S5.2 to obtain the time-varying natural wind speed time history data, which is used as the wind load subsequently applied to the finite element model.

7. The method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake according to claim 6 is characterized in that: The load applied to the finite element model established in S1 as described in S6 specifically includes: Using the ACEL command of ANSYS finite element software, the seismic wave working condition is set according to the rotation angle, and the wind load working condition is set according to the wind attack angle. The seismic wave acceleration data a′ obtained in S4.5 formula (5) is converted to x , a′ y , a′ z The wind loads obtained in S5.4 are applied to the finite element model of the bridge in the construction stage and the finite element model of the bridge in the completion stage, respectively.

8. The method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake according to claim 7 is characterized in that: The calculation of the dynamic response value under the combined action of earthquake and wind loads as described in S7 specifically includes the following sub-steps: S7.1 uses transient analysis as the analysis type and determines the time step based on the frequency characteristics of seismic waves, the fluctuating wind characteristics, and the vibration period of the bridge structure; S7.2 Based on the natural frequencies obtained in S3, calculate the Rayleigh damping parameters α and β and use ANSYS software to proportionally distribute the damping ratio to the mass term and the stiffness term; S7.3 takes the time period for the combined action of earthquake and wind loads as the total solution time; S7.4 Based on the parameters obtained in S7.1-S7.3, use ANSYS software to determine the displacement and internal force response values ​​of the three-dimensional suspension bridge structure to be evaluated under the combined action of earthquake and wind loads.

9. The method for evaluating the dynamic response of a long-span suspension bridge under the combined action of wind and earthquake according to claim 8 is characterized in that: The use of ORIGIN software to plot and analyze the internal force and displacement response values ​​as described in S8 specifically includes the following sub-steps: S8.1 Import the displacement and internal force response data obtained in S7.4 into the ORIGIN software and plot the horizontal tower top displacement diagrams for the three-dimensional suspension bridge to be evaluated during the construction and completion stages. S8.2 Compare the maximum horizontal tower top displacement and safety factor during the construction and completion phases with the allowable values ​​in the code: If the maximum horizontal tower top displacement is less than tower height / 100 and the safety factor is greater than 2.5, the bridge structure of the three-dimensional suspension bridge to be evaluated meets the requirements and does not require reinforcement; otherwise, the bridge structure of the three-dimensional suspension bridge to be evaluated does not meet the requirements, and the superstructure of the bridge tower of the three-dimensional suspension bridge to be evaluated needs to be inspected or reinforced.

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