A comfort assessment method for hanger arch bridges based on dynamic pedestrian load model

Abstract

The present invention discloses a method for evaluating the comfort of a suspension arch bridge based on a dynamic pedestrian load model, which belongs to the technical field of bridge engineering and structural dynamics, and includes: S1, constructing a finite element model of a suspension arch bridge; S2, establishing a regional dynamic pedestrian load model; S3, based on the finite element model of the suspension arch bridge, performing dynamic response analysis in combination with pedestrian loads, analyzing the acceleration response, frequency response and displacement response of the set nodes; S4, evaluating the comfort of the suspension arch bridge according to the acceleration response, frequency response and displacement response. This method analyzes the dynamic response of the bridge and quantitatively evaluates the comfort level of the bridge by simulating the time and space distribution of pedestrian loads in different regions; the present invention improves the evaluation accuracy, avoids the resonance risk of the step frequency and the structural fundamental frequency, and provides a scientific basis for bridge design and safe operation.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering and structural dynamics, and in particular relates to a comfort assessment method for a hanger arch bridge based on a dynamic walking load model. Background Art

[0002] At present, with the popularity of large-scale events (such as horse racing) and urban pedestrian traffic, the performance of bridges under large-scale crowd dynamic loads has attracted widespread attention. Especially for hanger arch bridges, due to their large flexibility and complex vibration modes, the bridge vibration caused by crowd walking loads may directly affect the comfort of the bridge and even endanger its safety.

[0003] At present, bridge comfort assessment mainly focuses on the vibration response caused by vehicle loads and wind loads, and there are relatively few studies on crowd loads. In particular, the dynamic characteristics of pedestrian loads are usually studied using a single step frequency or fixed load model. This simplified assumption is difficult to fully reflect the behavioral characteristics of large-scale crowds. Crowd load models generally use step frequency as the core parameter, ignoring the impact of crowd density, synchronization, and time dynamic distribution on bridge vibration; based on this, the existing bridge comfort assessment has the following shortcomings:

[0004] Insufficient walking load models: Existing walking load models are mostly based on the uniform distribution assumption and lack the description of non-uniform loads in special scenarios such as marathons.

[0005] Comfort assessment methods are lagging behind: Traditional comfort assessment is mainly based on simplified static or quasi-dynamic methods, which do not fully consider the complex dynamic response of hanger arch bridges.

[0006] Lack of dynamic coupling research: Existing methods usually analyze vertical loads and horizontal loads separately, failing to reflect the dynamic coupling effect between the two. Summary of the invention

[0007] In view of the fact that the bridge comfort assessment methods in the prior art fail to fully consider the influence of dynamic loads, group behavior and multi-dimensional vibration response, the present invention provides a hanger arch bridge comfort assessment method based on a walking load model, which solves the problems of inaccurate assessment and insufficient consideration of factors in traditional assessment methods under actual crowd loads.

[0008] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a method for evaluating the comfort of a hanger arch bridge based on a dynamic walking load model, comprising the following steps:

[0009] S1. Construct the finite element model of the hanger arch bridge;

[0010] S2. Establish a regional dynamic pedestrian load model;

[0011] S3. Based on the finite element model of the hanger arch bridge, the dynamic response analysis is carried out in combination with the pedestrian load to analyze the acceleration response, frequency response and displacement response of the set nodes;

[0012] S4. Evaluate the comfort of the hanger arch bridge based on acceleration response, frequency response and displacement response.

[0013] Furthermore, the step S1 includes the following sub-steps:

[0014] S11. Bridge geometry modeling for the suspender arch bridge;

[0015] S12. Perform dynamic analysis on the modeled bridge and calculate the natural frequency and vibration mode of the bridge;

[0016] S13. According to the calculated natural frequency and vibration mode, finite element analysis is performed to obtain the stiffness matrix, mass matrix and damping matrix of the bridge, and then the finite element model of the hanger arch bridge is obtained.

[0017] Furthermore, the step S2 includes the following sub-steps:

[0018] S21, dividing the bridge into multiple areas and calculating the equivalent number of people;

[0019] S22, determining the walking frequency of pedestrians in each area;

[0020] S23. Calculate the vertical load and horizontal load according to the step frequency, equivalent number of people and reduction factor in the area;

[0021] S24, dynamically load the horizontal load and vertical load of different areas, simulate the temporal and spatial changes of the step frequency and density of each area, and complete the establishment of the regional dynamic walking load model;

[0022] Furthermore, in step S21, the equivalent number of people in each divided area for:

[0023]

[0024] In the formula, represents the population density of the area, Indicates the area of ​​a region;

[0025] In step S22, in each area, i The walking pace of a pedestrian Follows a normal distribution ,in, represents the average cadence of the area, represents the standard deviation of the cadence;

[0026] In step S23, the vertical load and horizontal load They are:

[0027]

[0028]

[0029] In the formula, Indicates i The reduction factor for pedestrians, represents the horizontal load scaling factor, Indicates the moment;

[0030] In step S24, the density change obtained by the spatiotemporal change simulation It is expressed as:

[0031]

[0032] Random step frequency distribution changes obtained by temporal and spatial variation simulation It is expressed as:

[0033]

[0034] In the formula, represents the population density of the area, represents the density attenuation coefficient, represents the step frequency attenuation coefficient, represents a random disturbance, represents the average cadence of the area, Represents the standard deviation of cadence.

[0035] Furthermore, the step S3 includes the following sub-steps:

[0036] S31. Solve the dynamic equation of the bridge according to the pedestrian load to obtain the dynamic response of the bridge;

[0037] S32. According to the dynamic response of the bridge, the acceleration response, displacement response and frequency response of the set nodes are calculated respectively.

[0038] Furthermore, in step S31, the dynamic equation of the bridge is:

[0039]

[0040] In the formula, represents the displacement of each node of the bridge, Indicates speed, represents acceleration, represents the walking load vector, represents the mass matrix of the bridge, represents the damping matrix of the bridge, represents the stiffness matrix of the bridge;

[0041] In step S32, the displacement and acceleration Perform time domain analysis respectively to obtain the corresponding displacement response and acceleration response ; For acceleration Perform Fourier transform to get the frequency response of the bridge .

[0042] Furthermore, in step S4, the vertical comfort, horizontal comfort, frequency comfort and displacement comfort of the suspension arch bridge are evaluated to obtain a comfort evaluation result of the suspension arch bridge.

[0043] Furthermore, in step S4, by calculating the maximum vertical acceleration of the mid-span point of the bridge , and the corresponding preset vertical acceleration standard value Compare and then evaluate the vertical comfort; among them, represents the function of vertical acceleration;

[0044] By calculating the maximum horizontal acceleration of the bridge , and the corresponding preset horizontal acceleration standard value Compare and then evaluate the comfort in horizontal direction; Represents a function of horizontal acceleration;

[0045] By determining the cadence and the bridge natural frequency The matching degree can then be used to evaluate the frequency comfort;

[0046] By calculating the maximum displacement of the bridge mid-span , and the corresponding preset displacement limit Compare and then evaluate the displacement comfort; among them, Indicates the mid-span position of the bridge at time t The displacement of Indicates the mid-span position of the bridge. Indicates the span of the bridge.

[0047] Furthermore, the comfort of the suspension arch bridge is evaluated through three dimensions: acceleration qualification, resonance risk and displacement qualification.

[0048] Among them, for acceleration qualification, when the maximum vertical acceleration is greater than the preset vertical acceleration standard value, it affects the vertical acceleration qualification; when the maximum horizontal acceleration is greater than the preset horizontal acceleration standard value, it affects the horizontal acceleration qualification;

[0049] For resonance risk, When , there is a risk of resonance, which affects comfort; It represents the tolerance range between the natural frequencies of the bridge in the step frequency domain;

[0050] For displacement eligibility, when the maximum displacement Exceeds the corresponding preset displacement limit When the displacement is unqualified, the comfort is affected.

[0051] The beneficial effects of the present invention are:

[0052] (1) The present invention uses a suspension arch bridge comfort assessment method based on a walking load model to accurately simulate the dynamic load effect of a large-scale crowd on the bridge and comprehensively evaluate the dynamic response of the bridge under different crowd densities and step frequency distributions.

[0053] (2) The present invention provides a new assessment method by combining the finite element model of the bridge with dynamic load analysis, which can effectively guide the design, operation and maintenance of the bridge.

[0054] (3) The present invention proposes a comfort assessment method based on regional and dynamic loading, which can not only be applied to large-scale crowd load scenarios such as marathon events and urban pedestrian traffic, but also provide a scientific basis for improving the comfort of bridges.

[0055] (4) The present invention fills the technical gap in the existing technology of insufficient integration of large-scale crowd load and bridge comfort assessment by combining mathematical models, dynamic response analysis and engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A flow chart of the comfort assessment method for a hanger arch bridge of a dynamic walking load model provided by the present invention.

[0057] Figure 2 This is a bridge safety analysis diagram combining acceleration, displacement and frequency response provided by the present invention. DETAILED DESCRIPTION

[0058] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0059] The embodiment of the present invention provides a method for evaluating the comfort of a suspender arch bridge based on a dynamic walking load model. Figure 1 As shown, the following steps are included:

[0060] S1. Construct the finite element model of the hanger arch bridge;

[0061] S2. Establish a regional dynamic pedestrian load model;

[0062] S3. Based on the finite element model of the hanger arch bridge, the dynamic response analysis is carried out in combination with the pedestrian load to analyze the acceleration response, frequency response and displacement response of the set nodes;

[0063] S4. Evaluate the comfort of the hanger arch bridge based on acceleration response, frequency response and displacement response.

[0064] Step S1 of the embodiment of the present invention includes the following sub-steps:

[0065] S11. Bridge geometry modeling for the suspender arch bridge;

[0066] Specifically, the geometric model of the bridge is constructed using the bridge design drawings and actual measurement data to clarify the bridge's span, cross-sectional dimensions, support locations, etc.;

[0067] S12. Perform dynamic analysis on the modeled bridge and calculate the natural frequency of the bridge and vibration modes ;

[0068] Among them, the finite element method (FEA) is used to perform dynamic analysis on the bridge, and the dynamic equation used is:

[0069]

[0070] In the formula, represents the displacement of each node of the bridge, Indicates speed, represents acceleration, represents the walking load vector, represents the mass matrix of the bridge, represents the damping matrix of the bridge, represents the stiffness matrix of the bridge;

[0071] S13. According to the calculated natural frequency and vibration mode, finite element analysis is performed to obtain the stiffness matrix, mass matrix and damping matrix of the bridge, and then the finite element model of the hanger arch bridge is obtained.

[0072] In step S2 of the embodiment of the present invention, a walking load model is established according to the walking characteristics of large-scale crowds such as marathon events, and the regional crowd density and step frequency distribution are considered to dynamically load the loads of different regions; based on this, step S2 of this embodiment includes the following sub-steps:

[0073] S21, dividing the bridge into multiple areas and calculating the equivalent number of people;

[0074] Among them, the equivalent number of people in each divided area for:

[0075]

[0076] In the formula, represents the population density of the area, Indicates the area of ​​a region;

[0077] S22, determining the walking frequency of pedestrians in each area;

[0078] In each region, i The walking pace of a pedestrian Follows a normal distribution ,in, represents the average cadence of the area, represents the standard deviation of the cadence;

[0079] S23. Calculate the vertical load and horizontal load according to the step frequency, equivalent number of people and reduction factor in the area;

[0080] The vertical load and horizontal load They are:

[0081]

[0082]

[0083] In the formula, Indicates i The reduction factor for pedestrians, It represents the horizontal load proportional factor, which usually ranges from 0.1 to 0.2 and is used to adjust the ratio of horizontal load to vertical load. Indicates the moment;

[0084] S24, dynamically load the horizontal load and vertical load of different areas, simulate the temporal and spatial changes of the step frequency and density of each area, and complete the establishment of the regional dynamic walking load model;

[0085] Among them, the density change obtained by simulating the spatiotemporal changes It is expressed as:

[0086]

[0087] Random step frequency distribution changes obtained by temporal and spatial variation simulation It is expressed as:

[0088]

[0089] In the formula, represents the population density of the area, represents the density attenuation coefficient, represents the step frequency attenuation coefficient, represents a random disturbance, represents the average cadence of the area, Represents the standard deviation of cadence.

[0090] In this embodiment, when calculating the horizontal load and vertical load, It is used to adjust the matching degree between the step frequency and the natural frequency of the bridge. When the step frequency is close to the natural frequency of the bridge, it will cause resonance effect, so the influence of the load will be amplified. The reduction factor can accurately reflect this effect and correct it in the load calculation. The calculation formula is:

[0091]

[0092] In the formula, represents the natural frequency of the bridge, Indicates the tolerance range between the natural frequencies of the bridge in the step frequency domain, which is used to define the matching condition.

[0093] Step S3 of the embodiment of the present invention includes the following sub-steps:

[0094] S31. Solve the dynamic equation of the bridge according to the pedestrian load to obtain the dynamic response of the bridge;

[0095] Specifically, the dynamic response of the bridge under pedestrian load is solved by the following dynamic equation:

[0096]

[0097] In the formula, represents the displacement of each node of the bridge, Indicates speed, represents acceleration, represents the walking load vector, represents the mass matrix of the bridge, represents the damping matrix of the bridge, represents the stiffness matrix of the bridge; where the pedestrian load vector Generated by the regional dynamic pedestrian load model and Integration is obtained, and and is the local load, representing the vertical and horizontal loads in each area, These local loads are mapped to the global nodes of the bridge and the relationship is analyzed through dynamic response;

[0098] S32. According to the dynamic response of the bridge, the acceleration response, displacement response and frequency response of the set nodes are calculated respectively.

[0099] In this embodiment, the set node is a node on the suspender arch bridge that has a high impact on comfort and is set in advance. Specifically, the displacement of the set node and acceleration Perform time domain analysis respectively to obtain the corresponding displacement response and acceleration response ; For acceleration Perform Fourier transform to get the frequency response of the bridge .

[0100] In step S4 of the embodiment of the present invention, the comfort evaluation result of the suspension arch bridge is obtained by evaluating the vertical comfort, horizontal comfort, frequency comfort and displacement comfort of the suspension arch bridge.

[0101] In one specific embodiment, the maximum vertical acceleration at the mid-span of the bridge is calculated by , and the corresponding preset vertical acceleration standard value Compare and then evaluate the vertical comfort; among them, represents the function of vertical acceleration;

[0102] By calculating the maximum horizontal acceleration of the bridge , and the corresponding preset horizontal acceleration standard value Compare and then evaluate the comfort in horizontal direction; Represents a function of horizontal acceleration;

[0103] By determining the cadence and the bridge natural frequency The matching degree can then be used to evaluate the frequency comfort;

[0104] By calculating the maximum displacement of the bridge mid-span , and the corresponding preset displacement limit Compare and then evaluate the displacement comfort; among them, Indicates the mid-span position of the bridge at time t The displacement of Indicates the mid-span position of the bridge. Indicates the span of the bridge.

[0105] In this embodiment, the comfort of the suspender arch bridge is evaluated respectively in three dimensions: acceleration qualification, resonance risk and displacement qualification.

[0106] Among them, for acceleration qualification, when the maximum vertical acceleration is greater than the preset vertical acceleration standard value, it affects the vertical acceleration qualification; when the maximum horizontal acceleration is greater than the preset horizontal acceleration standard value, it affects the horizontal acceleration qualification;

[0107] For resonance risk, When , there is a risk of resonance, which affects comfort; It represents the tolerance range between the natural frequencies of the bridge in the step frequency domain;

[0108] For displacement eligibility, when the maximum displacement Exceeds the corresponding preset displacement limit When the displacement is unqualified, the comfort is affected.

[0109] In an embodiment of the present invention, a case study of a group of people crossing a bridge for a marathon based on the above-mentioned evaluation method is provided.

[0110] During a marathon event, the bridge may be subjected to dynamic loads generated by a large number of participants passing by. This load is unevenly distributed over time and place, and has strong volatility and frequency characteristics, which may cause resonance or excessive displacement of the bridge, thereby affecting the safety and comfort of the bridge. Therefore, the dynamic response analysis of the bridge under the crowd load of the marathon is particularly important. In this embodiment, a dynamic load analysis is performed on a 30-meter-long prestressed concrete simply supported beam bridge. Considering the crowd load that the bridge may encounter during the marathon event, a dynamic walking load model is used for simulation, such as Figure 2 As shown, a comprehensive analysis of the safety and comfort of the bridge is conducted by combining regional load simulation, dynamic response analysis, resonance risk assessment, and displacement comfort assessment. The analysis and assessment results are as follows:

[0111] Resonance risk assessment: Through frequency response analysis, no resonance risk was found in the bridge, and the load frequency was not close to the natural frequency of the bridge, indicating that the bridge would not resonate under the marathon crowd load.

[0112] Displacement comfort assessment: The displacement of the bridge under the maximum load did not exceed the displacement limit (0.02 meters), indicating that the bridge can still maintain good user comfort during the passage of marathon crowds.

[0113] Load distribution: Load analysis shows that the middle area of ​​the bridge bears a larger load, while the loads at both end areas are smaller, reflecting the concentrated characteristics of the marathon crowd.

[0114] Based on the above analysis process, the dynamic response of the 30-meter prestressed concrete simply supported beam bridge under the marathon crowd load was successfully evaluated based on the dynamic pedestrian load model, regional load simulation, multi-dimensional dynamic response analysis, resonance risk assessment and displacement comfort assessment; the results show that the bridge can safely carry the crowd load during the marathon event without resonance or excessive displacement, meeting the comfort requirements. Therefore, this method provides a comprehensive and accurate analysis tool for the safety assessment of bridges during large-scale crowd activities, which has important engineering application value.

[0115] The present invention uses a hanger arch bridge comfort assessment method based on a walking load model to accurately simulate the dynamic load effect of a large-scale crowd on the bridge and comprehensively evaluate the dynamic response of the bridge under different crowd densities and step frequency distributions.

[0116] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0117] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A comfort assessment method for a suspender arch bridge based on a dynamic walking load model, characterized in that: The following steps are involved: S1. Construct the finite element model of the hanger arch bridge; S2. Establish a regional dynamic pedestrian load model, which includes the following steps: S21, dividing the bridge into multiple areas and calculating the equivalent number of people; S22, determining the walking frequency of pedestrians in each area; S23. Calculate the vertical load and horizontal load according to the step frequency, equivalent number of people and reduction factor in the area; S24, dynamically load the horizontal load and vertical load of different areas, simulate the temporal and spatial changes of the step frequency and density of each area, and complete the establishment of the regional dynamic walking load model; S3. Based on the finite element model of the hanger arch bridge, the dynamic response analysis is carried out in combination with the pedestrian load to analyze the acceleration response, frequency response and displacement response of the set nodes; S4. Evaluate the comfort of the hanger arch bridge based on acceleration response, frequency response and displacement response.

2. The comfort assessment method for a suspender arch bridge based on a dynamic walking load model according to claim 1 is characterized in that: The step S1 comprises the following sub-steps: S11. Bridge geometry modeling for the suspender arch bridge; S12. Perform dynamic analysis on the modeled bridge and calculate the natural frequency and vibration mode of the bridge; S13. According to the calculated natural frequency and vibration mode, finite element analysis is performed to obtain the stiffness matrix, mass matrix and damping matrix of the bridge, and then the finite element model of the hanger arch bridge is obtained.

3. The comfort assessment method for a suspender arch bridge based on a dynamic walking load model according to claim 1 is characterized in that: In step S21, the equivalent number of people in each divided area for: In the formula, represents the population density of the area, Indicates the area of ​​a region; In step S22, in each area, i The walking pace of a pedestrian Follows a normal distribution ,in, represents the average cadence of the area, represents the standard deviation of the cadence; In step S23, the vertical load and horizontal load They are: In the formula, Indicates i The reduction factor for pedestrians, represents the horizontal load scaling factor, Indicates the moment; In step S24, the density change obtained by the spatiotemporal change simulation It is expressed as: Random step frequency distribution changes obtained by temporal and spatial variation simulation It is expressed as: In the formula, represents the population density of the area, represents the density attenuation coefficient, represents the step frequency attenuation coefficient, represents a random disturbance, represents the average cadence of the area, Represents the standard deviation of cadence.

4. The comfort assessment method for a suspender arch bridge based on a dynamic walking load model according to claim 1 is characterized in that: The step S3 comprises the following sub-steps: S31. Solve the dynamic equation of the bridge according to the pedestrian load to obtain the dynamic response of the bridge; S32. According to the dynamic response of the bridge, the acceleration response, displacement response and frequency response of the set nodes are calculated respectively.

5. The comfort assessment method for a suspender arch bridge based on a dynamic walking load model according to claim 4 is characterized in that: In step S31, the dynamic equation of the bridge is: In the formula, represents the displacement of each node of the bridge, Indicates speed, represents acceleration, represents the walking load vector, represents the mass matrix of the bridge, represents the damping matrix of the bridge, represents the stiffness matrix of the bridge; In step S32, the displacement and acceleration Perform time domain analysis respectively to obtain the corresponding displacement response and acceleration response ; For acceleration Perform Fourier transform to get the frequency response of the bridge .

6. The comfort assessment method for a suspender arch bridge based on a dynamic walking load model according to claim 1 is characterized in that: In step S4, the vertical comfort, horizontal comfort, frequency comfort and displacement comfort of the suspension arch bridge are evaluated to obtain the comfort evaluation result of the suspension arch bridge.

7. The comfort assessment method for a suspender arch bridge based on a dynamic walking load model according to claim 6 is characterized in that: In step S4, the maximum vertical acceleration of the bridge mid-span is calculated , and the corresponding preset vertical acceleration standard value Compare and then evaluate the vertical comfort; among them, Represents a function of vertical acceleration; By calculating the maximum horizontal acceleration of the bridge , and the corresponding preset horizontal acceleration standard value Compare and then evaluate the comfort in horizontal direction; represents the function of horizontal acceleration; By determining the cadence and the bridge natural frequency The matching degree can then be used to evaluate the frequency comfort; By calculating the maximum displacement of the bridge mid-span , and the corresponding preset displacement limit Compare and then evaluate the displacement comfort; among them, Indicates the mid-span position of the bridge at time t The displacement of Indicates the mid-span position of the bridge. Indicates the span of the bridge.

8. The comfort assessment method for a suspender arch bridge based on a dynamic walking load model according to claim 7 is characterized in that: The comfort of the suspender arch bridge is evaluated through three dimensions: acceleration qualification, resonance risk and displacement qualification. Among them, for acceleration qualification, when the maximum vertical acceleration is greater than the preset vertical acceleration standard value, it affects the vertical acceleration qualification; when the maximum horizontal acceleration is greater than the preset horizontal acceleration standard value, it affects the horizontal acceleration qualification; For resonance risk, When , there is a risk of resonance, which affects comfort; It represents the tolerance range between the natural frequencies of the bridge in the step frequency domain; For displacement eligibility, when the maximum displacement Exceeds the corresponding preset displacement limit When the displacement is unqualified, the comfort is affected.

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