A method for calculating pedestrian load of a curved bridge considering human-bridge coupling effect

Abstract

The application discloses a kind of arc bridge pedestrian load calculation methods considering human bridge coupling action, belong to bridge dynamics technical field.Considering the influence of human bridge mass ratio on the fundamental frequency of human bridge coupling system, frequency reduction coefficient is determined;Frequency-load reduction coefficient value method for arc bridge is established, based on human bridge coupling effect and the influence of arc bridge nonlinearity on the dynamic response of human bridge coupling system, load reduction coefficient for arc bridge is proposed;The equivalent number of pedestrians on arc bridge, load reduction coefficient corresponding to natural frequency and frequency reduction coefficient are integrated, and the pedestrian load of arc bridge under different crowd density levels is calculated.The application considers human bridge coupling effect, establishes a pedestrian load calculation method suitable for arc bridge design stage, and improves the accuracy of human-induced vibration response analysis of arc bridge.

Description

Technical Field

[0001] This invention relates to the field of bridge dynamics technology, and in particular to a method for calculating pedestrian loads on curved bridges that takes into account the coupling effect between pedestrians and bridges. Background Technology

[0002] With increasing attention being paid to improving urban image and landscape design, pedestrian bridges are gradually developing towards lightweight, long-span, and aesthetically pleasing irregular structures. Pedestrian bridges have low natural frequencies and exhibit significant nonlinearity, making pedestrian-induced vibration response analysis and comfort control difficult and complex. With the improvement of pedestrian bridge design standards and the substantial increase in bridge structural strength, pedestrian comfort has become an issue of equal importance to bridge safety. Currently, the pedestrian load models used in domestic and international bridge design codes do not adequately consider the interaction between pedestrians and the bridge structure, nor do they address curved pedestrian bridges, leading to significant discrepancies between code results and actual measurements. Therefore, considering the coupling relationship between pedestrians and the bridge structure, and specifically for the increasingly common curved pedestrian bridges, establishing a simplified calculation method for pedestrian loads on curved bridges that considers the pedestrian-bridge coupling effect is essential for the engineering design of pedestrian bridges. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating pedestrian loads on curved bridges that considers the coupling effect between pedestrians and bridges. This method simplifies the calculation of pedestrian loads on curved bridges by taking into account the coupling effect, and at the same time improves the accuracy of dynamic response analysis of curved bridges.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A method for calculating pedestrian loads on an arc bridge considering pedestrian-bridge coupling includes:

[0006] Obtain basic information about the curved bridge and determine the pedestrian density level on the curved bridge; the basic information includes: the mass of the curved bridge, the loading area of ​​the curved bridge, and the natural frequency of the curved bridge;

[0007] Based on the mass of the curved bridge, the loading area of ​​the curved bridge, and the population density level, the influence of the human-bridge mass ratio on the fundamental frequency of the human-bridge coupling system is considered, and the frequency reduction factor is determined.

[0008] Determine the values ​​of the load reduction factor for different frequencies of curved bridges, and establish a frequency-load reduction factor line graph;

[0009] Based on the natural frequency of the curved bridge, the load reduction factor corresponding to the natural frequency can be obtained by looking up the frequency-load reduction factor line graph.

[0010] Determine the equivalent number of pedestrians on the curved bridge based on the aforementioned crowd density level;

[0011] The pedestrian load of the arched bridge at the crowd density level is calculated based on the equivalent number of pedestrians on the arched bridge, the load reduction factor corresponding to the natural frequency, and the frequency reduction factor.

[0012] By repeating the above steps under multiple preset population density levels, the pedestrian load of the curved bridge under different population density levels can be obtained.

[0013] A pedestrian load calculation system for an arc bridge considering pedestrian-bridge coupling effects includes:

[0014] The information module acquisition block is used to acquire basic information about the curved bridge and determine the pedestrian density level on the curved bridge; the basic information includes: the mass of the curved bridge, the loading area of ​​the curved bridge, and the natural frequency of the curved bridge;

[0015] The frequency reduction factor determination module is used to determine the frequency reduction factor based on the mass of the curved bridge, the loading area of ​​the curved bridge, and the crowd density level, taking into account the influence of the human-bridge mass ratio on the fundamental frequency of the human-bridge coupling system.

[0016] The line graph creation module is used to determine the values ​​of the load reduction factor at different frequencies of curved bridges and to create a frequency-load reduction factor line graph.

[0017] The load reduction factor acquisition module is used to obtain the load reduction factor corresponding to the natural frequency of the curved bridge by looking up the frequency-load reduction factor line graph.

[0018] The equivalent number of pedestrians determination module is used to determine the equivalent number of pedestrians on the curved bridge based on the crowd density level.

[0019] The pedestrian load calculation module is used to calculate the pedestrian load of the arc bridge under the crowd density level based on the equivalent number of pedestrians on the arc bridge, the load reduction factor corresponding to the natural frequency, and the frequency reduction factor.

[0020] The loop module is used to repeat the above steps under multiple preset crowd density levels to obtain the pedestrian load of the curved bridge under different crowd density levels.

[0021] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0022] This invention discloses a method for calculating pedestrian loads on curved bridges considering pedestrian-bridge coupling. It considers the influence of the pedestrian-bridge mass ratio on the fundamental frequency of the pedestrian-bridge coupling system and determines a frequency reduction factor. A method for determining the frequency-load reduction factor for curved bridges is established. Based on the influence of pedestrian-bridge coupling and the nonlinearity of the curved bridge on the dynamic response of the pedestrian-bridge coupling system, a load reduction factor for curved bridges is proposed. By combining the equivalent number of pedestrians on the curved bridge, the load reduction factor corresponding to the natural frequency, and the frequency reduction factor, the pedestrian load on the curved bridge under different crowd density levels is calculated. This invention considers pedestrian-bridge coupling and establishes a simplified calculation method for pedestrian loads applicable to curved bridges, improving the accuracy of pedestrian-induced vibration response analysis of curved bridges. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 A flowchart of a method for calculating pedestrian load on an arc bridge considering the coupling effect between pedestrians and the bridge, provided in an embodiment of the present invention;

[0025] Figure 2 The frequency-load reduction factor line graph provided for embodiments of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] This invention, based on pedestrian-bridge coupling system analysis, proposes a method for calculating pedestrian loads on curved pedestrian bridges (arc bridges) that considers pedestrian-bridge coupling. It determines the uniformly distributed simplified pedestrian loads acting on the bridge (arc bridge) under different crowd density levels, enabling rapid calculation of the dynamic response of the curved bridge at specific crowd densities and assessing whether the bridge's comfort level meets standards. Based on the current standard "Standard for Vibration Loads of Buildings," and building upon the load calculation method for straight bridges, this invention fully considers the influence of the pedestrian-bridge mass ratio on the fundamental frequency of the pedestrian-bridge coupling system, the influence of the nonlinear characteristics of the curved bridge itself on the dynamic response of the pedestrian-bridge coupling system, and the influence of pedestrian load uncertainty on the dynamic response of the pedestrian-bridge coupling system. A frequency reduction factor is introduced to reflect the influence of the pedestrian-bridge mass ratio. Furthermore, considering the influence of pedestrian-bridge coupling and the nonlinearity of the curved bridge on the dynamic response of the coupling system, a load reduction factor for curved pedestrian bridges is proposed.

[0028] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] like Figure 1 As shown in the figure, an embodiment of the present invention provides a method for calculating pedestrian loads on an arc bridge considering the coupling effect between pedestrians and the bridge, comprising:

[0030] Step 1: Obtain the basic information of the curved bridge and determine the pedestrian density level on the curved bridge; the basic information includes: the mass of the curved bridge, the loading area of ​​the curved bridge, and the natural frequency of the curved bridge.

[0031] Obtain the basic design parameters of the curved bridge, calculate the bridge's mass, loading area, and natural frequency, and determine the population density level.

[0032] Step 2: Based on the mass of the curved bridge, the loading area of ​​the curved bridge, and the population density level, consider the influence of the human-bridge mass ratio on the fundamental frequency of the human-bridge coupling system, and determine the frequency reduction factor.

[0033] The frequency reduction factor κ is calculated based on the mass ratio of the human bridge:

[0034]

[0035] In the formula: β represents the ratio of human bridge mass; d represents the population density value corresponding to the population density level (Ped / m²). 2 As specified in the regulations; A represents the bridge loading area (m²). 2 );m p This indicates the weight of a single person, which can be taken as 70 kg; M B Indicates the quality of the bridge.

[0036] Note: Pedestrian mass distribution alters the fundamental frequency of the pedestrian-bridge coupling system, causing it to decrease. The greater the number of pedestrians, i.e., the higher the pedestrian-to-bridge mass ratio, the greater the impact on the fundamental frequency. To consider the influence of the pedestrian-to-bridge mass ratio β on the fundamental frequency of the system, a frequency reduction factor is introduced.

[0037] Step 3: Determine the load reduction factor for different frequencies of the curved bridge and establish a frequency-load reduction factor line graph.

[0038] Pedestrian movement on a bridge not only provides dynamic excitation to the bridge but also acts as a "mini damper" as a biological system, reducing the dynamic response of the pedestrian-bridge coupled system. Curved bridges, due to their shape, exhibit significant nonlinearity, making simplified pedestrian load calculation methods for straight bridges unsuitable. Therefore, considering the nonlinearity of curved bridges, the uncertainty of pedestrian loads, and the influence of pedestrians as SMD (Spring-Mass-Damper) models on the bridge's maximum acceleration response, the method for determining the load reduction factor is adjusted, and load reduction factors suitable for curved pedestrian bridges are proposed, as shown in Table 1.

[0039] Table 1. Load Reduction Factor Values

[0040]

[0041] Establish a frequency-load reduction factor line graph as follows: Figure 2 As shown. Compared with the existing frequency-load reduction factor line graph, the main adjustments are:

[0042] First, reduce the maximum value of the load reduction factor to 0.6, that is, when the fundamental frequency range is 1.7 to 2.1 Hz, the load reduction factor is 0.6;

[0043] Second, the frequency range of the first falling segment remains unchanged at 2.1–2.3 Hz, but the upper and lower limits are adjusted from 1 and 0.25 to 0.6 and 0.5.

[0044] Third, when the fundamental frequency range is 2.3 to 2.4 Hz, the load reduction factor is taken as 0.5;

[0045] Fourth, the frequency range of 2.4 to 2.5 Hz is set as the rising segment, increasing from a minimum value of 0.5 to 0.6;

[0046] Fifth, the original load reduction factor for the frequency range of 2.5 to 4.2 Hz is increased from 0.25 to 0.6.

[0047] See Figure 2The frequency-load reduction factor line graph includes: a first linear ascending segment, a first linear plateau segment, a first linear descending segment, a second linear plateau segment, a second linear ascending segment, a third linear plateau segment, and a second linear descending segment connected in sequence.

[0048] The frequency range of the first linear rising segment is 1.25Hz to 1.7Hz. The load reduction factor is 0 at 1.25Hz and 0.6 at 1.7Hz.

[0049] The frequency range of the first straight-line stationary segment is 1.7Hz to 2.1Hz, and the load reduction factor for the first straight-line stationary segment is 0.6.

[0050] The frequency range of the first linear descent segment is 2.1Hz to 2.3Hz. The load reduction factor is 0.6 at 2.1Hz and 0.5 at 2.3Hz.

[0051] The frequency range of the second straight-line stationary segment is 2.3Hz to 2.4Hz, and the load reduction factor for the second straight-line stationary segment is 0.5.

[0052] The frequency range of the second linear rising segment is 2.4Hz to 2.5Hz. The load reduction factor is 0.5 at 2.4Hz and 0.6 at 2.5Hz.

[0053] The frequency range of the third straight-line stationary segment is 2.5Hz to 4.2Hz, and the load reduction factor for the third straight-line stationary segment is 0.6.

[0054] The frequency range of the second linear descent segment is 4.2Hz to 4.6Hz. The load reduction factor is 0.6 at 4.2Hz and 0 at 4.6Hz.

[0055] Step 4: Based on the natural frequency of the curved bridge, obtain the load reduction factor corresponding to the natural frequency by looking up the frequency-load reduction factor line graph.

[0056] The load reduction factor corresponding to the natural frequency can be obtained from the frequency-load reduction factor line graph.

[0057] When a certain natural frequency of the curved bridge is located at Figure 2 When the frequency range is specified, the modal loading method is used to load the arc bridge for this mode.

[0058] Step 5: Determine the equivalent number of pedestrians on the curved bridge based on the crowd density level.

[0059] The method for calculating the equivalent number of pedestrians γ′ is as follows:

[0060] When pedestrian density (crowd density) is less than 1.0 Ped / m 2 hour:

[0061]

[0062] When the pedestrian density is not less than 1.0 Ped / m 2 hour:

[0063]

[0064] In the formula: ξ represents the structural damping ratio.

[0065] The calculation method for the equivalent number of pedestrians is based on the reference GB / T 51228-2017 Standard for Vibration Loads of Buildings (with explanatory notes).

[0066] Step 6: Calculate the pedestrian load of the curved bridge under the crowd density level based on the equivalent number of pedestrians on the curved bridge, the load reduction factor corresponding to the natural frequency, and the frequency reduction factor.

[0067] The pedestrian load calculation formula applicable to the design phase of curved pedestrian bridges is as follows:

[0068] F(t)=γ′ψ′κF b cos(2πf p t) (4)

[0069] In the formula: γ′ is the equivalent number of pedestrians, calculated according to formula (2) or (3); ψ′ is the load reduction factor, calculated according to... Figure 2 Values; κ is the frequency reduction factor, calculated according to equation (1); F b This represents the load amplitude generated by a single person, with a vertical force of 280N, a transverse force of 35N, and a longitudinal force of 140N; f p The pedestrian gait frequency is typically taken as the natural frequency of a certain order of the pedestrian bridge within the gait frequency sensitivity range. F b and f p References cited: GB / T 51228-2017 Standard for Vibration Loads of Buildings (with explanatory notes).

[0070] Step 7: Repeat the above steps under multiple preset crowd density levels to obtain the pedestrian load of the curved bridge under different crowd density levels.

[0071] The effectiveness of the method of the present invention will be verified below.

[0072] A dynamic response analysis model of the pedestrian-bridge coupled system is established based on the pedestrian SMD model:

[0073] A pedestrian-bridge coupled system was established, in which each pedestrian was modeled using SMD (Surface Mount Device) elements, and the bridge was modeled using shell elements. The pedestrian load was simplified to a fifth-order Fourier series. The pedestrian step frequency followed a normal distribution with a mean of 1.77 and a standard deviation of 0.149, and the phase angle followed a uniform distribution in the range of [-π, π]. The pedestrians were arranged according to the conditions that would cause the bridge to produce the most unfavorable response, and the entire process of the pedestrians crossing the bridge was simulated.

[0074] Monte Carlo simulation was used to obtain the results of three different radii of curvature (33.3m, 66.7m, and 100m) of curved bridges under three different population densities (0.9 Ped / m²). 2 1.0Ped / m 2 1.1Ped / m 2 The maximum acceleration response value under the simplified calculation formula is used as a reference for comparison.

[0075] Taking an arched bridge with a radius of curvature of 33.3m, a deck width of 5m, and a span of 40m as an example, the maximum acceleration response of the bridge was calculated by comparing the method used in the current specifications for straight pedestrian bridges with the method proposed in this invention, thus verifying the feasibility and rationality of the proposed method. The results are shown in Table 2. The results show that the maximum acceleration response of the pedestrian bridge caused by human-induced vibration, obtained by the load calculation formula for the arched pedestrian bridge proposed in this invention, is much smaller than the calculation results obtained by the current specifications for straight pedestrian bridges. This error pattern is consistent with the results of dynamic response analysis on the one hand, and with the error pattern of the measured results of the human-induced vibration response of an actual straight pedestrian bridge and its calculation results in the literature "Study on Vibration Characteristics of Pedestrian Bridge Considering Human-Structure Coupling" and the standards of various countries. That is, the measured human-induced vibration response of the pedestrian bridge is much smaller than the calculation results of the current standards of various countries. This verifies the rationality and effectiveness of the method of this invention. The detailed information of the literature "Study on Vibration Characteristics of Pedestrian Bridge Considering Human-Structure Coupling" is: Wang Caifeng. Study on Vibration Characteristics of Pedestrian Bridge Considering Human-Structure Coupling. Beijing Institute of Technology, 2017.

[0076] Table 2 Comparison of calculation results between current standards and the method of this invention.

[0077]

[0078] To implement the methods corresponding to the above embodiments and achieve the corresponding functions and technical effects, a pedestrian load calculation system for curved bridges considering the coupling effect between pedestrians and bridges is provided below, including:

[0079] The information acquisition module is used to acquire basic information about the curved bridge and determine the pedestrian density level on the curved bridge. The basic information includes: the mass of the curved bridge, the loading area of ​​the curved bridge, and the natural frequency of the curved bridge.

[0080] The frequency reduction factor determination module is used to determine the frequency reduction factor based on the mass of the curved bridge, the loading area of ​​the curved bridge, and the crowd density level, taking into account the influence of the human-bridge mass ratio on the fundamental frequency of the human-bridge coupling system.

[0081] The line graph creation module is used to determine the load reduction factor values ​​for different curved bridge frequencies and to create a frequency-load reduction factor line graph.

[0082] The load reduction factor acquisition module is used to obtain the load reduction factor corresponding to the natural frequency of the curved bridge by looking up the frequency-load reduction factor line graph.

[0083] The equivalent number of pedestrians determination module is used to determine the equivalent number of pedestrians on the curved bridge based on the crowd density level.

[0084] The pedestrian load calculation module is used to calculate the pedestrian load of the arc bridge under the crowd density level based on the equivalent number of pedestrians on the arc bridge, the load reduction factor corresponding to the natural frequency, and the frequency reduction factor.

[0085] The loop module is used to repeat the above steps under multiple preset crowd density levels to obtain the pedestrian load of the curved bridge under different crowd density levels.

[0086] The pedestrian load calculation system for curved bridges considering the coupling effect between pedestrians and bridges provided in the embodiments of the invention is similar in working principle and beneficial effect to the pedestrian load calculation method for curved bridges considering the coupling effect between pedestrians and bridges described in the above embodiments. Therefore, it will not be described in detail here. For details, please refer to the introduction of the above method embodiments.

[0087] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0088] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for calculating pedestrian loads on an arc bridge considering pedestrian-bridge coupling, characterized in that, include: Obtain basic information about the curved bridge and determine the pedestrian density level on the curved bridge; The basic information includes: the mass of the arc bridge, the loading area of ​​the arc bridge, and the natural frequency of the arc bridge; Based on the mass of the curved bridge, the loaded area of ​​the curved bridge, and the crowd density level, and considering the influence of the pedestrian-bridge mass ratio on the fundamental frequency of the pedestrian-bridge coupling system, a frequency reduction factor is determined; the formula for calculating the frequency reduction factor is as follows: and In the formula, Indicates the frequency reduction factor; Indicates the ratio of human to bridge mass; This indicates the population density value corresponding to the population density level; Indicates the loaded area of ​​the curved bridge; Indicates the mass of a single person; Indicates the mass of the curved bridge; Determine the values ​​of the load reduction factor for different frequencies of curved bridges, and establish a frequency-load reduction factor line graph; Based on the natural frequency of the curved bridge, the load reduction factor corresponding to the natural frequency can be obtained by looking up the frequency-load reduction factor line graph. Determine the equivalent number of pedestrians on the curved bridge based on the aforementioned crowd density level; Based on the equivalent number of pedestrians on the curved bridge, the load reduction factor corresponding to the natural frequency, and the frequency reduction factor, the pedestrian load of the curved bridge at the specified crowd density level is calculated; the formula for calculating the pedestrian load is as follows: In the formula, express Pedestrian load at any time This indicates the amplitude of the load force generated by a single person. Pedestrian cadence; Indicates the equivalent number of people in a row; This is the load reduction factor; By repeating the above steps under multiple preset population density levels, the pedestrian load of the curved bridge under different population density levels can be obtained.

2. The method for calculating pedestrian loads on curved bridges considering pedestrian-bridge coupling as described in claim 1, characterized in that, The formula for determining the load reduction factor at different frequencies for curved bridges is as follows: ； In the formula, The frequency of the arc bridge.

3. The method for calculating pedestrian loads on curved bridges considering pedestrian-bridge coupling as described in claim 2, characterized in that, The frequency-load reduction factor line graph includes: a first linear rising segment, a first linear stable segment, a first linear falling segment, a second linear stable segment, a second linear rising segment, a third linear stable segment, and a second linear falling segment connected in sequence. The frequency range of the first linear rising segment is 1.25Hz~1.7Hz. The load reduction factor is 0 at 1.25Hz and 0.6 at 1.7Hz. The frequency range of the first straight-line stationary segment is 1.7Hz to 2.1Hz, and the load reduction factor for the first straight-line stationary segment is 0.

6. The frequency range of the first linear descent segment is 2.1Hz~2.3Hz. The load reduction factor is 0.6 at 2.1Hz and 0.5 at 2.3Hz. The frequency range of the second linear stationary segment is 2.3Hz~2.4Hz, and the load reduction factor for the second linear stationary segment is 0.

5. The frequency range of the second linear rising segment is 2.4Hz~2.5Hz. The load reduction factor is 0.5 at 2.4Hz and 0.6 at 2.5Hz. The frequency range of the third straight-line stationary segment is 2.5Hz to 4.2Hz, and the load reduction factor for the third straight-line stationary segment is 0.

6. The frequency range of the second linear descent segment is 4.2Hz to 4.6Hz. The load reduction factor is 0.6 at 4.2Hz and 0 at 4.6Hz.

4. The method for calculating pedestrian loads on curved bridges considering pedestrian-bridge coupling as described in claim 2, characterized in that, Based on the aforementioned crowd density level, the equivalent number of pedestrians on the curved bridge is determined, specifically including: Based on the aforementioned population density level, according to the formula Calculate the equivalent number of people; where, This indicates the structural damping ratio.

5. The method for calculating pedestrian loads on curved bridges considering pedestrian-bridge coupling as described in claim 1, characterized in that, Based on the equivalent number of pedestrians on the curved bridge, the load reduction factor corresponding to the natural frequency, and the frequency reduction factor, the pedestrian load of the curved bridge at the specified crowd density level is calculated, followed by: Dynamic analysis of the curved bridge was performed based on the pedestrian load under the aforementioned crowd density level to obtain the maximum acceleration response of the curved bridge under pedestrian load. The maximum acceleration response is used as a comfort index of the curved bridge under the population density to be analyzed. The comfort level of the curved bridge is assessed based on the aforementioned comfort index to determine whether it meets the standards.

6. A pedestrian load calculation system for an arc bridge considering pedestrian-bridge coupling, characterized in that, include: The information acquisition module is used to acquire basic information about the curved bridge and determine the pedestrian density level on the curved bridge. The basic information includes: the mass of the arc bridge, the loading area of ​​the arc bridge, and the natural frequency of the arc bridge; The frequency reduction factor determination module is used to determine the frequency reduction factor based on the mass of the curved bridge, the loading area of ​​the curved bridge, and the crowd density level, taking into account the influence of the human-bridge mass ratio on the fundamental frequency of the human-bridge coupling system; the calculation formula for the frequency reduction factor is: and In the formula, Indicates the frequency reduction factor; Indicates the ratio of human to bridge mass; This indicates the population density value corresponding to the population density level; Indicates the loaded area of ​​the curved bridge; Indicates the mass of a single person; Indicates the mass of the curved bridge; The line graph creation module is used to determine the values ​​of the load reduction factor at different frequencies of curved bridges and to create a frequency-load reduction factor line graph. The load reduction factor acquisition module is used to obtain the load reduction factor corresponding to the natural frequency of the curved bridge by looking up the frequency-load reduction factor line graph. The equivalent number of pedestrians determination module is used to determine the equivalent number of pedestrians on the curved bridge based on the crowd density level. The pedestrian load calculation module is used to calculate the pedestrian load of the curved bridge at the specified crowd density level based on the equivalent number of pedestrians on the curved bridge, the load reduction factor corresponding to the natural frequency, and the frequency reduction factor; the calculation formula for the pedestrian load is: In the formula, express Pedestrian load at any time This indicates the amplitude of the load force generated by a single person. Pedestrian cadence; Indicates the equivalent number of people in a row; This is the load reduction factor; The loop module is used to repeat the above steps under multiple preset crowd density levels to obtain the pedestrian load of the curved bridge under different crowd density levels.

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