Railway continuous beam bridge transverse earthquake force simulation calculation method

Abstract

The application discloses a kind of railway continuous beam bridge lateral seismic force simulation calculation method, comprising the following steps: obtaining railway continuous beam bridge structure basic information;Simplify main beam mass distribution;The conversion mass of train live load is calculated and is evenly distributed to beam section two ends;Simplify main beam lateral stiffness;The agglomerate mass of bridge pier conversion to main beam centroid is calculated;The equivalent stiffness of bridge pier-ground foundation series connection model is calculated;The vibration characteristics of each order mode of single mode model are calculated;The correction coefficient of mode shape participation coefficient of single mode model is calculated;Bridge pier lateral seismic force is calculated.The application constructs continuous beam bridge lateral seismic force single mode simulation calculation model;Mode shape participation coefficient is corrected, and mode shape lateral seismic force is calculated according to response spectrum method and displacement equal principle, and railway continuous beam bridge lateral seismic force calculation result is obtained through mode superposition principle.The application solves the problem of railway continuous beam bridge lateral seismic force calculation.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology in the transportation industry, and specifically relates to a method for simulating and calculating the transverse seismic force of a railway continuous beam bridge. Background Technology

[0002] In recent years, my country's high-speed railway development and construction have progressed rapidly. The interconnected high-speed rail network plays an increasingly important role in facilitating public travel and promoting regional economic development, representing a significant aspect of my country's infrastructure construction. In my country's high-speed railway projects, bridges typically account for 70% or more of the total, and the design and construction quality of bridge structures largely determines the overall quality of the high-speed railway project. The design of railway bridge structures must consider numerous load types and combinations, among which seismic loads are a crucial component. In my country and worldwide, the damage caused by large and medium-sized earthquakes is severe for both highway and railway bridge structures. Due to the uncertainty of the spatiotemporal distribution and intensity of seismic loads, accurately assessing their destructive effects on structures is not easy. Therefore, a correct understanding and examination of the effects of earthquakes on railway bridge structures is essential to ensuring the quality of bridge structural design.

[0003] The vast majority of existing high-speed railway bridge structures in my country are concrete structures, with structural forms divided into simply supported beams and continuous beams. Simply supported beams are of standard span, precast and cast in a beam yard before erection. Continuous beam structures typically use three-span continuous beams with fixed spans, the most common span types being (32+48+32)m, (40+56(64)+40)m, (48+80+48)m, (60+100+60)m, and (72+128+72)m. These types of continuous beam structures are widely used in high-speed railway lines. Using standard span continuous beams can significantly reduce the workload of design calculations and drafting, while also shortening the construction period and saving on project costs.

[0004] In the calculation of seismic forces for continuous beam railway bridges, the general approach is to establish a full-bridge finite element model or to use a simplified algorithm specified in the current seismic design code for railway engineering. However, the former requires establishing a full-bridge finite element model for each continuous beam construction point, resulting in a large workload for modeling and calculation; the latter simplified algorithm is derived from simply supported beam structures, and while the calculation model is simple, its accuracy is low for continuous beam structures with complex structures and high coupling between components.

[0005] To address the aforementioned issues, it is essential to develop a simulation calculation method for lateral seismic forces applicable to railway continuous beam structures. This would improve the accuracy of lateral seismic force calculations and the design efficiency of railway continuous beam bridges, thereby systematically solving the problem of seismic force calculation for railway continuous beam bridges. Summary of the Invention

[0006] This invention is proposed to solve the problems existing in the prior art, and its purpose is to provide a method for simulating and calculating the transverse seismic force of a railway continuous beam bridge.

[0007] The technical solution of this invention is: a method for simulating and calculating the lateral seismic force of a continuous railway beam bridge, comprising the following steps:

[0008] A. Obtain basic structural information of railway continuous beam bridges;

[0009] B. Based on the basic structural information of the railway continuous beam bridge, it is divided into multiple different beam segments to simplify the mass distribution of the main beam;

[0010] C. Calculate the equivalent mass of the train's live load and distribute it evenly to both ends of the beam segment;

[0011] D. Based on the end sections of the beam segments, simplify the transverse stiffness of the main beam;

[0012] E. Based on the basic structural information of the railway continuous beam bridge, calculate the mass of the piers converted to the centroid of the main beam;

[0013] F. Calculate the equivalent stiffness of the pier-foundation series model based on the accumulated mass;

[0014] G calculates the vibration characteristics of each mode of the single-mode model based on steps B and F;

[0015] H. Correction coefficients for calculating the modal participation coefficients of the single-mode model based on step G;

[0016] I. Calculate the lateral seismic force on the bridge piers.

[0017] Furthermore, in step A, the basic information of the railway continuous beam bridge structure is obtained, which includes the bridge type, load, material grade, seismic motion parameters, main beam geometric parameters, and pier geometric parameters.

[0018] Furthermore, step B simplifies the mass distribution of the main beams based on the basic structural information of the railway continuous beam bridge. The specific process is as follows:

[0019] First, the main beam is divided into axes of symmetry;

[0020] Then, take one side of the structural axis of symmetry and divide it into multiple different beam segments according to the changes in the main beam cross section;

[0021] Then, within the segments of different beam segments, the parts with drastic changes in cross-section are simplified into variable cross-section segments, while the other parts are simplified into constant cross-section segments;

[0022] Then, the mass of the constant cross-section segment is concentrated at the nodes on both sides of the segment, and the mass of the variable cross-section segment is concentrated at the nodes on both sides and the middle node of the segment. The same treatment is done on the other side of the axis of symmetry.

[0023] Finally, the mass of each beam segment is distributed to the two end nodes according to the principle that the allocated mass is proportional to the end cross-sectional area.

[0024] Furthermore, step C calculates the equivalent mass of the train's live load and distributes it evenly to both ends of the beam segment. The specific process is as follows:

[0025] First, the equivalent mass of the train's live load is calculated based on the principle of unchanged dynamic characteristics;

[0026] Then, the calculated equivalent mass is distributed to both ends of the beam segment or to both ends and the middle node of the beam segment according to the beam segment divided in step B.

[0027] Furthermore, step D simplifies the transverse stiffness of the main beam based on the end sections of the beam segment. The specific process is as follows:

[0028] First, take the end section of the beam segment in step B as the main section, calculate the transverse moment of inertia of the main section, and calculate the average value.

[0029] Then, the lateral moments of inertia of all major sections were changed to their average values, while the parameters of other sections remained unchanged.

[0030] Furthermore, step E calculates the mass of the piers converted to the center of mass of the main beam based on the basic information of the railway continuous beam bridge structure.

[0031] First, assume that the deformation of the bridge pier consists of two broken lines, and apply a lateral unit force to the top of the bridge pier.

[0032] Then, the ratio of the lateral deformation at the bottom and half the calculated height of the pier body to the lateral deformation at the point where the unit force is applied is calculated when considering the foundation deformation, and the equivalent mass coefficient is calculated accordingly.

[0033] Finally, the mass conversion factor is multiplied by the pier mass to obtain the mass of the pier converted to the center of mass of the main beam.

[0034] Furthermore, step F calculates the equivalent stiffness of the pier-foundation series model based on the accumulated mass. The specific process is as follows:

[0035] First, establish a calculation model for a single bridge pier and foundation;

[0036] Then, a lateral unit force is applied at the top of the pier, the deformation at that point is calculated, and the reciprocal of the deformation is taken to obtain the lateral equivalent stiffness of the pier-foundation series model.

[0037] Finally, the longitudinal and vertical components of the equivalent stiffness are directly taken as the corresponding stiffness components of the foundation.

[0038] Furthermore, step G calculates the vibration characteristics of each mode of the single-mode model, and the specific process is as follows:

[0039] First, list the dynamic equilibrium equations for the single-mode model and define the dynamic matrix;

[0040] Then, the vibration iteration method is used to iteratively calculate each vibration mode.

[0041] Furthermore, step H calculates the correction factor for the mode participation factor of the single-mode model, and the specific process is as follows:

[0042] First, calculate the modal participation factor of the original continuous beam bridge model;

[0043] Then, the modal participation factor of the single-mode model is calculated;

[0044] Finally, the ratio of the modal participation factors of the two models is used to obtain the correction factor for the modal participation factor of the single-mode model.

[0045] Furthermore, step I calculates the lateral seismic force on the bridge piers, and the specific process is as follows:

[0046] First, a distributed concentrated force model of the bridge pier is established, with multiple concentrated forces acting from the top to the bottom of the pier to ensure that the displacement at the top of the pier is the same as the modal displacement. The concentrated forces acting on the pier are calculated, and the lateral shear force and bending moment at the bottom of the pier are obtained by superimposing the concentrated forces acting on the pier body.

[0047] Then, the seismic force of the vibration mode is calculated using the response spectrum method. By superimposing the seismic forces of each vibration mode, the lateral seismic force of the bridge pier is obtained, which is the lateral seismic force of the railway continuous beam bridge.

[0048] The beneficial effects of this invention are as follows:

[0049] This invention addresses the problem of calculating lateral seismic forces in continuous railway beam bridges. It proposes a simplified modeling method for continuous railway beam bridge structures, constructing a single-mode simulation model for lateral seismic forces. Based on dynamic principles and the modal iteration method, the vibration characteristics of the simulation model are calculated, and the modal participation coefficient is corrected. The modal lateral seismic forces are calculated using the response spectrum method and the principle of equal displacement. Finally, the calculation results of the lateral seismic forces in the continuous railway beam bridge are obtained through the modal superposition principle.

[0050] This invention addresses the calculation problem of continuous railway beam bridges in the transportation sector, accurately simulating the dynamic simulation calculation model of continuous railway beam bridges and solving the problem of calculating lateral seismic forces. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0052] Figure 2 This is a schematic diagram of a continuous railway beam bridge model in this invention;

[0053] Figure 3 This is a schematic diagram of the main beam mass distribution method and distribution position in this invention;

[0054] Figure 4 This is a schematic diagram of the bridge pier deformation model in this invention;

[0055] Figure 5 This is a schematic diagram of the single vibration mode model in this invention;

[0056] Figure 6 This is a schematic diagram of the pier distribution force calculation model in this invention;

[0057] Figure 7 This is a schematic diagram of the SAP2000 numerical model of the railway continuous beam bridge in Embodiment 1 of the present invention. Detailed Implementation

[0058] The present invention will now be described in detail with reference to the accompanying drawings and embodiments:

[0059] like Figures 1 to 7 As shown, a simulation calculation method for lateral seismic force of a railway continuous beam bridge includes the following steps:

[0060] A. Obtain basic structural information of railway continuous beam bridges;

[0061] B. Based on the basic structural information of the railway continuous beam bridge, it is divided into multiple different beam segments to simplify the mass distribution of the main beam;

[0062] C. Calculate the equivalent mass of the train's live load and distribute it evenly to both ends of the beam segment;

[0063] D. Based on the end sections of the beam segments, simplify the transverse stiffness of the main beam;

[0064] E. Based on the basic structural information of the railway continuous beam bridge, calculate the mass of the piers converted to the centroid of the main beam;

[0065] F. Calculate the equivalent stiffness of the pier-foundation series model based on the accumulated mass;

[0066] G calculates the vibration characteristics of each mode of the single-mode model based on steps B and F;

[0067] H. Correction coefficients for calculating the modal participation coefficients of the single-mode model based on step G;

[0068] I. Calculate the lateral seismic force on the bridge piers.

[0069] In step A, the basic information of the railway continuous beam bridge structure is obtained. This basic information includes the bridge type, load, material grade, seismic motion parameters, main beam geometric parameters, and pier geometric parameters.

[0070] Step B simplifies the main beam mass distribution based on the basic structural information of the railway continuous beam bridge. The specific process is as follows:

[0071] First, the main beam is divided into axes of symmetry;

[0072] Then, take one side of the structural axis of symmetry and divide it into multiple different beam segments according to the changes in the main beam cross section;

[0073] Then, within the segments of different beam segments, the parts with drastic changes in cross-section are simplified into variable cross-section segments, while the other parts are simplified into constant cross-section segments;

[0074] Then, the mass of the constant cross-section segment is concentrated at the nodes on both sides of the segment, and the mass of the variable cross-section segment is concentrated at the nodes on both sides and the middle node of the segment. The same treatment is done on the other side of the axis of symmetry.

[0075] Finally, the mass of each beam segment is distributed to the two end nodes according to the principle that the allocated mass is proportional to the end cross-sectional area.

[0076] Step C calculates the equivalent mass of the train's live load and distributes it evenly to both ends of the beam segment. The specific process is as follows:

[0077] First, the equivalent mass of the train's live load is calculated based on the principle of unchanged dynamic characteristics;

[0078] Then, the calculated equivalent mass is distributed to both ends of the beam segment or to both ends and the middle node of the beam segment according to the beam segment divided in step B.

[0079] Step D simplifies the transverse stiffness of the main beam based on the end sections of the beam segment. The specific process is as follows:

[0080] First, take the end section of the beam segment in step B as the main section, calculate the transverse moment of inertia of the main section, and calculate the average value.

[0081] Then, the lateral moments of inertia of all major sections were changed to their average values, while the parameters of other sections remained unchanged.

[0082] Step E: Calculate the mass of the piers converted to the center of mass of the main beam based on the basic information of the railway continuous beam bridge structure;

[0083] First, assume that the deformation of the bridge pier consists of two broken lines, and apply a lateral unit force to the top of the bridge pier.

[0084] Then, the ratio of the lateral deformation at the bottom and half the calculated height of the pier body to the lateral deformation at the point where the unit force is applied is calculated when considering the foundation deformation, and the equivalent mass coefficient is calculated accordingly.

[0085] Finally, the mass conversion factor is multiplied by the pier mass to obtain the mass of the pier converted to the center of mass of the main beam.

[0086] Step F calculates the equivalent stiffness of the pier-foundation series model based on the accumulated mass. The specific process is as follows:

[0087] First, establish a calculation model for a single bridge pier and foundation;

[0088] Then, a lateral unit force is applied at the top of the pier, the deformation at that point is calculated, and the reciprocal of the deformation is taken to obtain the lateral equivalent stiffness of the pier-foundation series model.

[0089] Finally, the longitudinal and vertical components of the equivalent stiffness are directly taken as the corresponding stiffness components of the foundation.

[0090] Step G calculates the vibration characteristics of each mode of the single-mode model. The specific process is as follows:

[0091] First, list the dynamic equilibrium equations for the single-mode model and define the dynamic matrix;

[0092] Then, the vibration iteration method is used to iteratively calculate each vibration mode.

[0093] Step H calculates the correction factor for the modal participation factor of the single-mode model. The specific process is as follows:

[0094] First, calculate the modal participation factor of the original continuous beam bridge model;

[0095] Then, the modal participation factor of the single-mode model is calculated;

[0096] Finally, the ratio of the modal participation factors of the two models is used to obtain the correction factor for the modal participation factor of the single-mode model.

[0097] Step I calculates the lateral seismic force on the bridge piers. The specific process is as follows:

[0098] First, a distributed concentrated force model of the bridge pier is established, with multiple concentrated forces acting from the top to the bottom of the pier to ensure that the displacement at the top of the pier is the same as the modal displacement. The concentrated forces acting on the pier are calculated, and the lateral shear force and bending moment at the bottom of the pier are obtained by superimposing the concentrated forces acting on the pier body.

[0099] Then, the seismic force of the vibration mode is calculated using the response spectrum method. By superimposing the seismic forces of each vibration mode, the lateral seismic force of the bridge pier is obtained, which is the lateral seismic force of the railway continuous beam bridge.

[0100] Specifically, in step A, the bridge type includes the number of bridge spans and the span of each span; its loads include the secondary dead load, train live load, and the weight of the simply supported beams in the side spans; its seismic parameters include the basic horizontal design acceleration and characteristic period; its main beam geometric parameters include the distance from the centroid of the cross-section at the side support and the middle support to the point of application of the train load on the superstructure, the cross-sectional area, and the lateral bending moment of inertia; its pier geometric parameters include the pier type (constrained abutment, open abutment, or pier), the length of the variable cross-section segment of each pier, the cross-sectional area at both ends of the variable cross-section segment and the lateral bending moment of inertia, the distance from the pier top to the centroid of the main beam, the additional mass at the pier top, the translational stiffness of the pier, the translational stiffness of the foundation, the rotational stiffness, and the translational-rotational coupling stiffness.

[0101] Specifically, step B involves dividing the railway continuous beam bridge into multiple different beam segments based on the basic structural information, simplifying the mass distribution of the main beam. The specific process is as follows:

[0102] The main beam of a railway continuous beam bridge has a variable cross-section. If all the cross-sectional dimensions of the main beam are considered, the workload of modeling and calculation will be greatly increased, but the calculation accuracy will not be improved much. Therefore, simplification is adopted.

[0103] First, since the main beams of the continuous beam bridge are all symmetrical structures, one side of the axis of symmetry is divided into multiple segments based on the changes in the cross-section of the main beam. The main beam sections with drastic cross-section changes are simplified into variable cross-section segments, while other sections are simplified into constant cross-section segments. The mass of the constant cross-section segments is concentrated at the nodes on both sides of the segment, while the mass of the variable cross-section segments is concentrated at the nodes on both sides and the middle node of the segment. The same treatment is applied to the other side of the axis of symmetry.

[0104] like Figure 3 The three-span continuous beam shown has its left side of the axis of symmetry divided into three segments from left to right: constant cross-section segment 1, variable cross-section segment 2, and variable cross-section segment 3. The constant cross-section segment is simplified to 2 nodes, and the variable cross-section segment is simplified to 3 nodes, thus simplifying the main beam into a model with 9 lumped mass nodes.

[0105] Then, the principle for distributing the mass of each beam segment to the two end nodes is that the distributed mass is proportional to the area of ​​the end cross section. If the ratio of the areas at both ends is:

[0106] A1:A2=r (1)

[0107] The quality ratio allocated to the two endpoints is:

[0108] m1:m2=(2r+1):(r+2) (2).

[0109] Specifically, step C calculates the equivalent mass of the train live load and distributes it evenly to both ends of the beam segment. When there is a train, the distributed mass of the train acting 2m above the rail surface needs to be converted to the centroid of the main beam, and the train mass is distributed to the concentrated mass nodes in the same way as the simplified method for the main beam. The specific process is as follows:

[0110] First, calculate the equivalent mass of the train's live load. The calculation of the train's mass must follow the principle of unchanged dynamic characteristics, that is, ensuring that the generalized mass remains unchanged in the original bridge model vibration equation. The calculation formula is as follows:

[0111]

[0112] In formula (3), m v For the distributed mass of the train; The following parameters are the vehicle mass and the modal displacement at the beam's center of mass, respectively, for calculating the vibration modes.

[0113] Then, the train mass converted to the center of mass of the main beam is distributed to both ends of the beam segment or to both ends and the middle node of the beam segment according to the beam segment divided in step B.

[0114] Specifically, step D simplifies the transverse stiffness of the main beam based on the end sections of the beam segment. In the transverse vibration of a continuous beam, the main main beam stiffness parameter affecting the transverse seismic response is the transverse moment of inertia I of the cross section. 22 Other parameters have minimal impact. The simplification of the main beam's lateral stiffness primarily addresses the lateral moment of inertia, and the specific process is as follows:

[0115] First, the end sections of the beam segments divided in step B are taken as the principal sections, and the transverse moments of inertia I of these principal sections are calculated respectively. 22 And calculate the average lateral moment of inertia.

[0116] Then, modify the lateral moments of inertia of all major sections to their average values. Other cross-sectional parameters remain unchanged.

[0117] Specifically, step E calculates the mass of the bridge piers converted to the center of mass of the main girder. The specific process is as follows:

[0118] First, assume the deformation of the bridge pier is a two-segment broken line model, such as... Figure 4 As shown, the lateral deformation of the pier top, midpoint, and bottom is selected for calculation, and its equivalent mass coefficient is:

[0119]

[0120] In formula (4), X f and These are the ratios of the lateral deformation at the pier base and half the calculated height of the pier body when a lateral unit force is applied to the pier top, taking into account foundation deformation, to the lateral deformation at the point where the unit force is applied.

[0121] Then, by multiplying the reduced mass coefficient obtained from formula (4) with the pier mass, we can obtain the mass of the pier converted to the center of mass of the main beam.

[0122] Specifically, step F calculates the equivalent stiffness of the pier-foundation series model. After simplifying the pier mass to the center of mass of the main beam in step E, its lateral stiffness and foundation stiffness need to be considered using the equivalent springs at the supports. The specific process is as follows:

[0123] First, establish a calculation model of a single pier and foundation, and apply a lateral unit force at the top of the pier to calculate the displacement at the top of the pier. The reciprocal of the displacement is then used to obtain the lateral equivalent stiffness of the pier-foundation series model.

[0124] Then, the longitudinal and vertical translational stiffness at the support has no effect on the calculation of the lateral seismic force, and can be directly taken as the corresponding stiffness of the foundation. Then, the equivalent springs of these three stiffness values ​​are added to the support.

[0125] Specifically, step G calculates the vibration characteristics of each mode of the single-mode model. The simplification from step B to step F yields a single-mode calculation model, such as... Figure 5 As shown. The specific process for calculating the vibration characteristics of each mode of this model is as follows:

[0126] First, according to the principle of modal superposition, the model displacement response v is the superposition of the displacement responses of all modes:

[0127]

[0128] The vibration characteristics of each mode can be calculated using the modal iteration method. The dynamic equilibrium equations for a single-mode model are as follows:

[0129]

[0130] Define the dynamic matrix as follows:

[0131] D = k -1 m (7)

[0132] The iterative calculation process can be represented as follows:

[0133]

[0134]

[0135] Then, through multiple iterations of calculation, the result of a certain vibration mode can be obtained:

[0136]

[0137] The same method can be used for iterative calculations of other vibration modes.

[0138] Specifically, step H calculates the correction factor for the modal participation factor of the single-mode model. The modal participation factor of the single-mode model will change compared to the original continuous beam model. To ensure calculation accuracy, the modal participation factor of the single-mode model needs to be corrected. The specific process is as follows:

[0139] First, the model simplification process always follows the principle of invariant structural dynamic characteristics, that is, it satisfies the principle of invariant generalized mass:

[0140]

[0141] In formula (11), and These represent the generalized mass of the superstructure and the generalized mass of the substructure piers, respectively. The formula for calculating the modal participation factor of the original continuous beam bridge model is:

[0142]

[0143] Then, the vibration participation factor of the single-mode model is calculated. Since the pier mass satisfies the generalized mass invariance principle, the pier mass and the distributed mass of the original continuous beam bridge model satisfy the following:

[0144]

[0145] Therefore, the formula for calculating the modal participation factor of a single-mode model is:

[0146]

[0147] Then, the ratio of the modal participation factors of the two models is the correction factor for the modal participation factor of the single-mode model:

[0148]

[0149] Specifically, step I calculates the lateral seismic force on the bridge piers, and the specific process is as follows:

[0150] First, based on the principle of equal displacement at the pier top, a distributed concentrated force model for the bridge pier is established, such as... Figure 6 As shown, multiple concentrated forces act from the top to the bottom of the pier, ensuring that the displacement at the top of the pier is the same as the modal displacement. Therefore, the concentrated force acting on the pier is...

[0151] u0 = F G δ1+ΣF i δ i (16)

[0152] In formula (16), the concentrated force F at the top of the pier is... G Concentrated force F distributed on the pier body i These are the inertial forces of the mass at that location, i.e.

[0153]

[0154]

[0155] Superimposing the inertial forces, the lateral shear force and bending moment acting on the bottom of the bridge pier are obtained as follows:

[0156] V m =F G +ΣF i (19)

[0157] M m =F G ·H+ΣF i ·h i (20)

[0158] Then, the seismic force of this mode is calculated using the response spectrum method:

[0159]

[0160]

[0161] In formulas (21) and (22), S a The value of the acceleration response spectrum corresponding to this mode shape is γ1, which is the mode participation coefficient and needs to be corrected using the correction coefficient obtained in step H.

[0162] Then, the seismic forces of each vibration mode are calculated separately and superimposed to obtain the lateral seismic forces of the bridge piers, which is the lateral seismic force of the railway continuous beam bridge.

[0163] In actual calculations, the dominant mode controlling the lateral seismic response can be selected by calculating the mode participation coefficient of each mode in the single-mode model. The lateral seismic force calculation result that meets the engineering accuracy requirements can be obtained by simply superimposing the seismic force of the dominant mode.

[0164] Example 1

[0165] The present invention was used to perform a comparative verification of the lateral seismic force calculation on a (32+48+32)m continuous beam bridge.

[0166] The design of the main beam of the continuous beam bridge is based on the general drawing "Tongqiao (2017) 2368-1" and the design of the piers is based on the general drawing "Sanqiaotong (2017) 4360-8-16". Figure 7 A schematic diagram of the numerical model of the continuous beam bridge built using the Sap2000 finite element software.

[0167] To better illustrate the problem, calculations were performed using two different operating conditions: with and without vehicles. In the case without vehicles, step C of the present invention was omitted, while the other steps remained unchanged.

[0168] The lateral seismic forces of the continuous beam bridge were calculated using Sap2000 finite element software and a program developed according to this invention, respectively. The results are compared in Table 1. In the table, Δu% represents the percentage difference between the first-order modal displacement calculated by the self-developed program and the first-order modal displacement calculated by Sap2000 software; Δe% represents the percentage difference between the lateral seismic force of the first-order mode calculated by the self-developed program and the seismic force of all orders calculated by Sap2000 software.

[0169] Table 1. Comparison of Calculation Results of Lateral Seismic Force for (32+48+32)m Continuous Beam Bridge

[0170]

[0171] As shown in Table 1, the calculation results of the first-order modal displacement using the program developed in this invention are very close to those calculated by Sap2000, with a maximum relative error of no more than 6%, meeting the engineering accuracy requirements. Similarly, when comparing the lateral seismic force of the first mode with the lateral seismic force of all modes in Sap2000 software, the maximum relative interpolation value of the program considering only the lateral seismic force of the first mode is 20.7% of that of pier #4 under the no-vehicle condition, while for the vehicle condition, the maximum relative interpolation value does not exceed 7%, also meeting the engineering accuracy requirements. The calculation results also show that the dominant mode controlling the lateral seismic response of this continuous beam bridge is the first mode, and high calculation accuracy can be obtained by calculating only the seismic force of this mode.

[0172] In summary, the simulation calculation method for transverse seismic force of railway continuous beam bridges described in this invention meets the requirements of actual engineering design calculations.

[0173] This invention addresses the problem of calculating lateral seismic forces in continuous railway beam bridges. It proposes a simplified modeling method for continuous railway beam bridge structures, constructing a single-mode simulation model for lateral seismic forces. Based on dynamic principles and the modal iteration method, the vibration characteristics of the simulation model are calculated, and the modal participation coefficient is corrected. The modal lateral seismic forces are calculated using the response spectrum method and the principle of equal displacement. Finally, the calculation results of the lateral seismic forces in the continuous railway beam bridge are obtained through the modal superposition principle.

[0174] This invention addresses the calculation problem of continuous railway beam bridges in the transportation sector, accurately simulating the dynamic simulation calculation model of continuous railway beam bridges and solving the problem of calculating lateral seismic forces.

Claims

1. A method for simulating and calculating lateral seismic forces in a continuous railway beam bridge, characterized in that: Includes the following steps: (A) Obtain basic structural information of railway continuous beam bridges; (B) Based on the basic information of the railway continuous beam bridge structure, it is divided into multiple different beam segments to simplify the distribution of the main beam mass; (C) Calculate the equivalent mass of the train live load and distribute it evenly to both ends of the beam segment; (D) Based on the end sections of the beam segments, simplify the transverse stiffness of the main beam; (E) Based on the basic structural information of the railway continuous beam bridge, calculate the mass of the piers converted to the centroid of the main beam; (F) Calculate the equivalent stiffness of the pier-foundation series model based on the accumulated mass; (G) Calculate the vibration characteristics of each mode of the single-mode model based on steps (B) and (F); (H) Calculate the correction factor for the mode participation factor of the single-mode model based on step (G); (I) Calculate the lateral seismic force on the bridge piers; Step (B) Based on the basic structural information of the railway continuous beam bridge, the mass distribution of the main beam is simplified. The specific process is as follows: First, the main beam is divided into axes of symmetry; Then, take one side of the structural axis of symmetry and divide it into multiple different beam segments according to the changes in the main beam cross section; Then, within different paragraphs, the parts with drastic changes in cross-section are simplified into variable cross-section paragraphs, while other parts are simplified into constant cross-section paragraphs; Then, the mass of the constant cross-section segment is concentrated at the nodes on both sides of the segment, and the mass of the variable cross-section segment is concentrated at the nodes on both sides and the middle node of the segment. The same treatment is done on the other side of the axis of symmetry. Finally, the mass of each beam segment is distributed to the two end nodes according to the principle that the allocated mass is proportional to the end cross-sectional area; Step (D) simplifies the transverse stiffness of the main beam based on the end sections of the beam segment. The specific process is as follows: First, take the end section of the beam segment in step (B) as the main section, calculate the transverse moment of inertia of the main section, and calculate the average value; Then, modify the lateral moments of inertia of all major sections to their average values, while keeping the parameters of other sections unchanged; Step (H) calculates the correction factor for the mode participation factor of the single-mode model. The specific process is as follows: First, calculate the modal participation factor of the original continuous beam bridge model; Then, the vibration participation factor of the single-mode model is calculated; Finally, the ratio of the mode participation factors of the two models yields the correction factor for the mode participation factor of the single-mode model. First, a distributed concentrated force model of the bridge pier is established, with multiple concentrated forces acting from the top to the bottom of the pier to ensure that the displacement at the top of the pier is the same as the modal displacement. The concentrated forces acting on the pier are calculated, and the lateral shear force and bending moment at the bottom of the pier are obtained by superimposing the concentrated forces acting on the pier body. Then, the seismic force of the vibration mode is calculated using the response spectrum method. By superimposing the seismic forces of each vibration mode, the lateral seismic force of the bridge pier is obtained, which is the lateral seismic force of the railway continuous beam bridge.

2. The method for simulating and calculating the transverse seismic force of a continuous railway beam bridge according to claim 1, characterized in that: In step (A), the basic information of the railway continuous beam bridge structure is obtained. The basic information of the railway continuous beam bridge structure includes bridge type, load, material grade, seismic motion parameters, main beam geometric parameters, and pier geometric parameters.

3. The method for simulating and calculating the transverse seismic force of a continuous railway beam bridge according to claim 1, characterized in that: Step (C) calculates the equivalent mass of the train's live load and distributes it evenly to both ends of the beam segment. The specific process is as follows: First, the equivalent mass of the train's live load is calculated based on the principle of unchanged dynamic characteristics; Then, the calculated equivalent mass is distributed to the two ends of the beam segment or to the two ends and the middle node of the beam segment according to the division in step (B).

4. The method for simulating and calculating the transverse seismic force of a continuous railway beam bridge according to claim 1, characterized in that: Step (E) Calculate the mass of the piers converted to the center of mass of the main beam based on the basic information of the railway continuous beam bridge structure; First, assume that the deformation of the bridge pier consists of two broken lines, and apply a lateral unit force to the top of the bridge pier. Then, the ratio of the lateral deformation at the bottom and half the calculated height of the pier body to the lateral deformation at the point where the unit force is applied is calculated when considering the foundation deformation, and the equivalent mass coefficient is calculated accordingly. Finally, the mass conversion factor is multiplied by the pier mass to obtain the mass of the pier converted to the center of mass of the main beam.

5. The method for simulating and calculating the transverse seismic force of a continuous railway beam bridge according to claim 1, characterized in that: Step (F) calculates the equivalent stiffness of the pier-foundation series model based on the accumulated mass. The specific process is as follows: First, establish a calculation model for a single bridge pier and foundation; Then, a lateral unit force is applied at the top of the pier, the deformation at that point is calculated, and the reciprocal of the deformation is taken to obtain the lateral equivalent stiffness of the pier-foundation series model. Finally, the equivalent stiffness longitudinal and vertical components are directly taken as the corresponding stiffness components of the foundation.

6. The method for simulating and calculating the transverse seismic force of a continuous railway beam bridge according to claim 1, characterized in that: Step (G) calculates the vibration characteristics of each mode of the single-mode model. The specific process is as follows: First, list the dynamic equilibrium equations for the single-mode model and define the dynamic matrix; Then, the vibration iteration method is used to iteratively calculate each vibration mode.

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