A conventional span continuous rigid frame beam end restraint design method
By adopting a standardized limit design method, the minimum lateral thrust stiffness of the limit device is obtained based on the comprehensive lateral stiffness of the beam end and the initial relative displacement. This solves the problem of excessive relative displacement in conventional span continuous rigid frame bridges, improves design efficiency and scientificity, and ensures the smoothness of the bridge track and traffic safety.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA RAILWAY MAJOR BRIDGE RECONNAISSANCE & DESIGN INSTITUTE CO LTD
- Filing Date
- 2026-04-10
- Publication Date
- 2026-07-31
AI Technical Summary
Under external loads, the beam ends of two adjacent main beams of conventional span continuous rigid frame bridges experience large relative displacements, exceeding the design specification limits. This affects the smoothness of the track and the safety of train operation. Existing design methods rely on complex overall finite element models and repeated trial calculations based on experience, resulting in low design efficiency and a lack of scientific rigor.
By determining the actual transverse dimensions of the piers based on the comprehensive transverse stiffness and initial relative displacement at the beam ends, the minimum transverse thrust stiffness of the limiting device is obtained. Through standardized calculation and verification processes, the actual transverse thrust stiffness is adjusted until it meets the design requirements, thereby verifying the strength of the limiting device and ensuring track smoothness and driving safety.
It improves design efficiency, ensures the smoothness of bridge tracks and driving safety, and replaces the traditional complex overall finite element model that relies on experience, thus realizing scientific and efficient limit design.
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Figure CN122490637A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of bridge engineering design, and in particular to a design method for end restraint of conventional span continuous rigid frame beams. Background Technology
[0002] In recent years, conventional span unsupported continuous rigid frame bridges have been widely used in railway and urban rail transit bridge engineering due to their ease of maintenance. This type of bridge typically consists of 2-4 spans per section, with each span measuring 30-40 meters. The piers and main beams are rigidly connected, eliminating the need for supports and maintenance facilities, thus significantly reducing operation and maintenance costs.
[0003] However, to release the internal forces caused by structural temperature, the piers of this bridge type are often designed to be relatively thin and flexible, forming independent, separate pier structures between each span. This structural form leads to significant relative displacement between the ends of adjacent main beams under external loads (such as temperature and train live loads). This displacement often exceeds the design specifications, posing a serious threat to the smoothness of the track and thus endangering traffic safety.
[0004] To control this excessive displacement, the preliminary solution adopted is to install lateral restraint devices at the beam ends. These devices allow the beam to expand and contract freely in the longitudinal direction while constraining its relative lateral displacement.
[0005] The relevant design methods typically require establishing a finite element model encompassing multiple bridge sections, considering the complex bending-torsional coupling between the main beams, piers, and foundations. Numerical simulations are then used to calculate the relative displacement response at the beam ends under various load combinations. During the design process, engineers must repeatedly adjust the stiffness parameters of the limiting device according to the allowable displacement values specified in the standards, determining a limiting device design scheme that meets the control requirements through multiple trial calculations. In practical applications, this method relies heavily on the designer's experience and judgment, and usually needs to be revised based on field test data. Summary of the Invention
[0006] This application provides a conventional span continuous rigid frame beam end limiting design method to solve the problem that the relative displacement limiting design between conventional span continuous rigid frame bridges requires the establishment of a complex overall model and relies on repeated trial calculations, resulting in low design efficiency and lack of scientific rigor.
[0007] A conventional span continuous rigid frame beam end limiting design method is provided, which includes: confirming the actual transverse dimensions of the pier based on the comprehensive lateral stiffness, initial relative displacement, and allowable relative displacement of the beam end; after confirming the actual transverse dimensions of the pier, obtaining the minimum lateral thrust stiffness of the limiting device based on the comprehensive lateral stiffness, initial relative displacement, and allowable relative displacement of the beam end; confirming the actual lateral thrust stiffness of the limiting device based on the minimum lateral thrust stiffness of the limiting device; obtaining the actual relative displacement after the limiting device is installed at the beam end based on the actual lateral thrust stiffness of the limiting device; and determining whether the actual lateral thrust stiffness meets the design requirements based on the allowable relative displacement and the actual relative displacement. If it does, verifying the strength of the limiting device and using the verified and qualified limiting device as the final design scheme; otherwise, adjusting the actual lateral thrust stiffness until it meets the requirements.
[0008] In some embodiments, the initial relative displacement includes the initial horizontal relative displacement and initial relative torsional angle caused by the lateral eccentric load at the front end of the beam before the limiting device is set, and the permissible relative displacement includes the permissible horizontal relative displacement and permissible relative torsional angle caused by the lateral eccentric load at the rear end of the beam after the limiting device is set.
[0009] In some embodiments, the actual transverse dimensions of the pier are determined based on the comprehensive lateral stiffness of the beam end, the initial relative displacement, and the allowable relative displacement. Specifically, this includes: obtaining the correction amount of the limiting device for the relative torsion angle of the beam end based on the comprehensive lateral stiffness of the beam end and the initial horizontal relative displacement; obtaining the verification relative torsion angle after setting the limiting device based on the initial relative torsion angle and the correction amount; and determining the actual transverse dimensions of the pier based on the verification relative torsion angle and the allowable relative torsion angle.
[0010] In some embodiments, the actual transverse dimension of the bridge pier is determined based on the calculated relative torsion angle and the allowable relative torsion angle. Specifically, this includes: comparing the calculated relative torsion angle and the allowable relative torsion angle to determine whether the transverse stiffness of the bridge meets the traffic safety requirements; if the calculated relative torsion angle is less than the allowable relative torsion angle, the transverse stiffness of the bridge is confirmed to meet the traffic safety requirements, and the current transverse dimension of the bridge pier is taken as the actual transverse dimension of the bridge pier; if the calculated relative torsion angle is greater than the allowable relative torsion angle, the transverse dimension of the bridge pier is adjusted to ensure that the transverse stiffness of the bridge meets the traffic safety requirements, and the adjusted transverse dimension of the bridge pier is taken as the actual transverse dimension of the bridge pier.
[0011] In some embodiments, the beam end comprehensive lateral stiffness includes lateral thrust stiffness and beam end comprehensive coupling stiffness, and the minimum lateral thrust stiffness of the limiting device is obtained based on the beam end comprehensive lateral stiffness, initial relative displacement, and allowable relative displacement. Specifically, this includes: obtaining a first thrust stiffness that meets the requirements of the beam end horizontal relative displacement based on the initial horizontal relative displacement, allowable horizontal relative displacement, and lateral thrust stiffness; obtaining a second thrust stiffness that meets the requirements of the beam end relative torsional angle based on the initial horizontal relative displacement, initial relative torsion angle, allowable relative torsion angle, lateral thrust stiffness, and beam end comprehensive coupling stiffness; and using the largest thrust stiffness value between the first and second thrust stiffness as the minimum lateral thrust stiffness of the limiting device.
[0012] In some embodiments, the actual lateral thrust stiffness of the limiting device is determined based on the minimum lateral thrust stiffness of the limiting device. Specifically, this includes: preliminarily determining the structural dimensions of the limiting device based on the minimum lateral thrust stiffness; obtaining the shear stiffness, bending stiffness, and thrust stiffness of the limiting device based on the preliminarily determined structural dimensions; obtaining the target lateral thrust stiffness based on the shear stiffness, bending stiffness, and thrust stiffness; and confirming the actual lateral thrust stiffness based on the target lateral thrust stiffness and the minimum lateral thrust stiffness.
[0013] In some embodiments, the actual lateral thrust stiffness is determined based on the target lateral thrust stiffness and the minimum lateral thrust stiffness. Specifically, this includes: comparing whether the target lateral thrust stiffness is greater than the minimum lateral thrust stiffness; if it is greater, then the target lateral thrust stiffness is taken as the actual lateral thrust stiffness; otherwise, the initially determined structural design dimensions are readjusted until the target lateral thrust stiffness is greater than the minimum lateral thrust stiffness.
[0014] In some embodiments, the actual relative displacement after the limiting device is installed at the beam end is obtained based on the actual lateral thrust stiffness of the limiting device. Specifically, this includes: obtaining the actual horizontal relative displacement based on the lateral thrust stiffness, the actual lateral thrust stiffness, and the initial horizontal relative displacement; obtaining the actual relative torsion angle based on the lateral thrust stiffness, the beam end comprehensive coupling stiffness, the actual lateral thrust stiffness, the initial horizontal relative displacement, and the initial relative torsion angle; and the actual relative displacement after the limiting device is installed at the beam end includes the actual horizontal relative displacement and the actual relative torsion angle.
[0015] In some embodiments, the determination of whether the actual lateral thrust stiffness meets the design requirements is based on the allowable relative displacement and the actual relative displacement. Specifically, this includes: comparing whether the allowable relative displacement is greater than the actual relative displacement; if it is greater, then confirming that the actual lateral thrust stiffness meets the design requirements; otherwise, readjusting the actual lateral thrust stiffness.
[0016] In some embodiments, verifying the strength of the limiting device specifically includes: obtaining the internal force of the limiting device based on the lateral thrust stiffness and the initial relative displacement; and verifying the strength of the limiting device based on the internal force of the limiting device.
[0017] The beneficial effects of the technical solution provided in this application include: This application provides a conventional span continuous rigid frame beam end limiting design method. First, the actual transverse dimensions of the pier are confirmed based on the comprehensive transverse stiffness of the beam end, the initial and allowable relative displacements. Second, the minimum transverse thrust stiffness of the limiting device is obtained and the actual transverse thrust stiffness is determined. Subsequently, the actual relative displacement after setting the limiting device is calculated and compared with the allowable relative displacement. If the requirements are met, the strength of the limiting device is further verified as qualified and used as the final design scheme. If the requirements are not met, the actual transverse thrust stiffness is adjusted until it meets the requirements. Through this standardized calculation and verification process, the traditional method of relying on complex overall finite element models and repeated trial calculations based on experience is replaced. This not only ensures track smoothness and driving safety, but also significantly improves design efficiency and the scientific nature of the scheme. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 The spatial overall stress model of the two-beam structure provided in this application embodiment; Figure 2 A stress model provided for illustrating one of the beams in this application embodiment; Figure 3 This is a schematic diagram of the overall steps provided for the embodiments of this application; Figure 4 A detailed flowchart illustrating the steps for S1 provided in this application embodiment; Figure 5 A detailed flowchart illustrating the steps involved in S2, provided for an embodiment of this application; Figure 6 A detailed flowchart illustrating the steps for S3 provided in this application embodiment. Detailed Implementation
[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0021] This application provides a conventional span continuous rigid frame beam end limiting design method, which can solve the problem in related technologies that the design of relative displacement limiting between conventional span continuous rigid frame track bridges requires the establishment of a complex overall model and relies on repeated trial calculations, resulting in low design efficiency and lack of scientific rigor.
[0022] Reference Figure 1-2 In the bridge design process, this application requires the establishment of a comprehensive calculation model for each span of beams for internal force analysis of the main beam, piers, and foundations. In the conventional span continuous rigid frame beam end-constraint design method of this application, a spatial overall force model for both spans of beams and a force model for one span of beams are established separately. Furthermore, in the overall force model, the bottom of the separated side piers at the beam joint between the two spans of beams should be considered as consolidated, while the foundation stiffness of the remaining piers should be considered.
[0023] Reference Figure 1-6 A conventional span continuous rigid frame beam end restraint design method, which includes S1: Based on the comprehensive lateral stiffness of the beam end, the initial relative displacement, and the allowable relative displacement, confirm the actual transverse dimensions of the bridge pier. The initial relative displacement includes the initial horizontal relative displacement and the initial relative torsional angle caused by the lateral eccentric load at the beam end before the installation of the limiting device, and are expressed as follows: and The lateral eccentric load at the beam end includes the lateral eccentric component of the moving load and the lateral eccentric component of the environmental effect. The lateral eccentric component of the moving load includes: the pier top displacement caused by train eccentric loading, the pier top displacement caused by centrifugal force, and the pier top displacement caused by swaying force; the lateral eccentric component of the environmental effect includes: the pier top displacement caused by lateral wind force and the pier top displacement caused by lateral temperature difference.
[0024] The specific methods for determining the initial horizontal relative displacement and initial relative torsional angle in the force model are as follows: Calculate the initial displacement of the train eccentric load on the tops of the piers on both sides of the beam joint:
[0025] Calculate the initial displacement of the centrifugal force at the top of the piers on both sides of the beam joint:
[0026] Calculate the initial displacement of the swaying force at the top of the piers on both sides of the beam joint:
[0027] Calculate the initial lateral wind displacement of the pier tops on both sides of the beam joint:
[0028] Calculate the initial lateral displacement of the pier tops at the beam joint due to temperature difference:
[0029] Initial horizontal relative displacement:
[0030] Initial relative twist angle:
[0031] The allowable relative displacement includes the allowable horizontal relative displacement and allowable relative torsional angle caused by the lateral eccentric load at the beam end after the limit device is installed, and are expressed as follows: and Both are upper limits, generally specified by national or industry standards. Designers may also appropriately reduce the standard values to take into account a certain safety redundancy.
[0032] In this step, based on the comprehensive lateral stiffness of the beam end, the initial relative displacement, and the allowable relative displacement, the actual transverse dimensions of the bridge pier are confirmed, specifically including: S10: Based on the comprehensive lateral stiffness of the beam end and the initial horizontal relative displacement, the correction amount of the limiting device to the relative torsional angle of the beam end is obtained, expressed by the formula:
[0033] in, C1 and C2 represent the combined lateral thrust stiffness of the beam ends at the joint between the two beams, and C1 and C2 represent the combined coupling stiffness of the two beam ends. By applying a horizontal force F of arbitrary magnitude to the beam end in the force model of one of the beams, the horizontal displacement of the corresponding beam end can be calculated based on the force model. and twist angle Then the overall transverse lateral lateral stiffness at the beam end is:
[0034] The combined coupling stiffness at the beam end is:
[0035] S11: Based on the initial relative torsion angle and the correction amount, obtain the verification relative torsion angle after setting the limit device, expressed by the formula:
[0036] S12: Based on the calculated relative torsion angle and the allowable relative torsion angle, confirm the actual transverse dimensions of the bridge piers. Specifically, this includes comparing the calculated relative torsion angle and the allowable relative torsion angle to determine whether the bridge's lateral stiffness meets traffic safety requirements; expressed by the formula:
[0037] If the calculated relative torsion angle is less than the allowable relative torsion angle, it is confirmed that the lateral stiffness of the bridge meets the traffic safety requirements, and the current transverse dimension of the pier is taken as the actual transverse dimension of the pier. If the calculated relative torsion angle is greater than the allowable relative torsion angle, the transverse dimension of the pier is adjusted to ensure that the lateral stiffness of the bridge meets the traffic safety requirements, and the adjusted transverse dimension of the pier is taken as the actual transverse dimension of the pier. After confirming that the lateral stiffness of the bridge meets the traffic safety requirements, it is indicated that the beam end can be controlled by setting a limit device.
[0038] S2: After confirming the actual transverse dimensions of the bridge pier, the minimum transverse lateral stiffness of the limiting device is obtained based on the comprehensive transverse stiffness of the beam end, the initial relative displacement, and the allowable relative displacement.
[0039] This step specifically includes: S20: Based on the initial horizontal relative displacement, allowable horizontal relative displacement, and lateral thrust stiffness, obtain the first thrust stiffness at the beam end that meets the requirements for horizontal relative displacement, expressed by the formula:
[0040] Among them, shilling , This is expressed as the actual horizontal relative displacement. Represented as the limit efficiency coefficient; S21: Based on the initial horizontal relative displacement, initial relative torsion angle, allowable relative torsion angle, lateral thrust stiffness, and beam end comprehensive coupling stiffness, obtain the second thrust stiffness that satisfies the requirement for the beam end relative torsion angle, expressed by the formula:
[0041] Among them, shilling , Expressed as the actual relative torsion angle, Represented as the limit efficiency coefficient; S22: The maximum thrust stiffness value between the first and second thrust stiffness is used as the minimum lateral thrust stiffness of the limiting device. This is done to simultaneously ensure that the horizontal relative displacement and relative torsional angle at the beam end do not exceed the allowable values. The minimum lateral thrust stiffness is... express.
[0042] S3: Based on the minimum lateral thrust stiffness of the limiting device, confirm the actual lateral thrust stiffness of the limiting device. This step specifically includes: S30: Based on the minimum lateral thrust stiffness, the structural dimensions of the limiting device are initially determined; specifically, based on the calculated minimum lateral thrust stiffness, the designer estimates the required cross-section or number of anchor bolts for the limiting device according to standard engineering design procedures, such as initially selecting a set of structural design dimensions, with a rectangular cross-section: =300x100mm, shear span: f=400mm, anchor bolt specifications on one side of the beam: 16 anchor bolts, φ22mm, the same on the other side; S31: Then, based on the initially determined structural dimensions, the shear stiffness, bending stiffness, and thrust stiffness of the limiting device are obtained, wherein: the shear stiffness is expressed as: Bending stiffness is expressed as: Thrust stiffness is expressed as ; S32: Based on shear stiffness, bending stiffness, and thrust stiffness, the target lateral thrust stiffness is obtained, expressed by the formula:
[0043] S33: Finally, based on the target lateral thrust stiffness and the minimum lateral thrust stiffness, the actual lateral thrust stiffness is confirmed. Specifically, this is done by directly comparing whether the target lateral thrust stiffness is greater than the minimum lateral thrust stiffness, expressed by the formula:
[0044] If the target lateral thrust stiffness is greater than the minimum lateral thrust stiffness, then the target lateral thrust stiffness is taken as the actual lateral thrust stiffness; otherwise, the initially confirmed structural design dimensions are readjusted until the target lateral thrust stiffness is greater than the minimum lateral thrust stiffness.
[0045] S4: The lateral thrust stiffness was calculated based on the above steps. Although the lateral thrust stiffness is greater than the minimum lateral thrust stiffness, the result is not intuitive enough. Further calculation of the actual relative displacement at the beam end is needed. This includes calculating the actual lateral thrust stiffness based on the limiting device and obtaining the actual relative displacement at the beam end after the limiting device is installed. This step specifically includes: S40: Based on the lateral thrust stiffness, actual lateral thrust stiffness, and initial horizontal relative displacement, the actual horizontal relative displacement is obtained, expressed by the formula:
[0046] S41: Based on the lateral thrust stiffness, beam end comprehensive coupling stiffness, actual lateral thrust stiffness, initial horizontal relative displacement, and initial relative torsion angle, the actual relative torsion angle is obtained, expressed by the formula:
[0047] The actual relative displacement after the beam end is fitted with a limiting device includes the actual horizontal relative displacement and the actual relative torsional angle, which are expressed as follows: and .
[0048] S5: Based on the allowable relative displacement and the actual relative displacement, determine whether the actual lateral thrust stiffness meets the design requirements. If it does, verify the strength of the limiting device and use the verified limiting device as the final design scheme; otherwise, adjust the actual lateral thrust stiffness until it meets the requirements. Specifically, determining whether the actual lateral thrust stiffness meets the design requirements based on the allowable relative displacement and the actual relative displacement includes: comparing whether the allowable relative displacement is greater than the actual relative displacement; if it is greater, confirm that the actual lateral thrust stiffness meets the design requirements; otherwise, readjust the actual lateral thrust stiffness. Readjusting the actual lateral thrust stiffness requires returning to the previous steps, reconfirming the structural design dimensions of the limiting device, and re-executing the calculation steps.
[0049] In this step, the strength of the limiting device is verified, specifically including: based on the lateral thrust stiffness and the initial relative displacement, the internal force of the limiting device is obtained, expressed by the formula:
[0050] Furthermore, based on the internal forces of the limiting device, the strength of the limiting device is verified, including but not limited to the cross-sectional shear stress calculation and the anchor bolt bearing capacity calculation. The cross-sectional shear stress calculation is expressed by the formula:
[0051] Where Q represents the internal force of the limiting device. Expressed as cross-sectional shear stress,
[0052] It is expressed as the allowable cross-sectional shear stress; the anchor bolt bearing capacity is checked by calculating the product of a single anchor bolt and the number of anchor bolts, obtaining the total bearing capacity, and determining whether the total bearing capacity is greater than the internal force of the limiting device.
[0053] If this application only focuses on whether the displacement at the beam end meets the standard, it may result in the design of a limiting device with excessive stiffness. Although the displacement meets the specifications, the huge thrust may cause the limiting device to be sheared, the shear stress to exceed the standard, or the pier to be damaged due to excessive local stress. Therefore, it is still necessary to review and ensure the safety of the bridge, that the displacement does not exceed the standard, and that the device itself is safe and does not fail.
[0054] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.
[0055] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0056] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.
Claims
1. A conventional span continuous rigid frame beam end limiting design method, characterized in that: It includes: Based on the comprehensive transverse stiffness of the beam end, the initial relative displacement, and the allowable relative displacement, the actual transverse dimensions of the bridge pier are confirmed. After confirming the actual transverse dimensions of the bridge piers, the minimum transverse thrust stiffness of the limiting device is obtained based on the comprehensive transverse stiffness of the beam end, the initial relative displacement, and the allowable relative displacement. Based on the minimum lateral thrust stiffness of the limiting device, the actual lateral thrust stiffness of the limiting device is determined. Based on the actual lateral thrust stiffness of the limiting device, the actual relative displacement after the limiting device is installed at the beam end is obtained. Based on the allowable relative displacement and the actual relative displacement, determine whether the actual lateral thrust stiffness meets the design requirements. If it does, verify the strength of the limiting device and use the verified limiting device as the final design scheme. Otherwise, adjust the actual lateral thrust stiffness until it meets the requirements.
2. The conventional span continuous rigid frame beam end limiting design method as described in claim 1, characterized in that: The initial relative displacement includes the initial horizontal relative displacement and initial relative torsional angle caused by the lateral eccentric load at the front beam end before the limiting device is set, and the permissible relative displacement includes the permissible horizontal relative displacement and permissible relative torsional angle caused by the lateral eccentric load at the rear beam end after the limiting device is set.
3. The conventional span continuous rigid frame beam end limiting design method as described in claim 2, characterized in that: Based on the comprehensive lateral stiffness of the beam ends, the initial relative displacement, and the allowable relative displacement, the actual transverse dimensions of the bridge piers are determined, specifically including: Based on the comprehensive lateral stiffness of the beam end and the initial horizontal relative displacement, the correction amount of the limiting device to the relative torsional angle of the beam end is obtained. Based on the initial relative torsion angle and the correction amount, obtain the verified relative torsion angle after setting the limit device; Based on the verification of the relative torsion angle and the allowable relative torsion angle, the actual transverse dimensions of the bridge piers are confirmed.
4. The conventional span continuous rigid frame beam end limiting design method as described in claim 3, characterized in that: Based on the verification of the relative torsion angle and the allowable relative torsion angle, the actual transverse dimensions of the bridge piers are confirmed, including: The relative torsion angle and the allowable relative torsion angle are compared and verified to determine whether the lateral stiffness of the bridge meets the requirements for traffic safety. If the calculated relative torsion angle is less than the allowable relative torsion angle, it is confirmed that the lateral stiffness of the bridge meets the traffic safety requirements, and the current transverse dimension of the pier is taken as the actual transverse dimension of the pier. If the calculated relative torsion angle is greater than the allowable relative torsion angle, the transverse dimensions of the piers are adjusted to ensure that the lateral stiffness of the bridge meets the requirements for traffic safety, and the adjusted transverse dimensions of the piers are taken as the actual transverse dimensions of the piers.
5. The conventional span continuous rigid frame beam end limiting design method as described in claim 2, characterized in that: The beam end comprehensive lateral stiffness includes lateral thrust stiffness and beam end comprehensive coupling stiffness. Based on the beam end comprehensive lateral stiffness, initial relative displacement, and allowable relative displacement, the minimum lateral thrust stiffness of the limiting device is obtained, specifically including: Based on the initial horizontal relative displacement, the allowable horizontal relative displacement and the lateral thrust stiffness, the first thrust stiffness that meets the requirements of the horizontal relative displacement at the beam end is obtained. Based on the initial horizontal relative displacement, initial relative torsion angle, allowable relative torsion angle, transverse thrust stiffness and beam end comprehensive coupling stiffness, the second thrust stiffness that meets the requirements of the beam end relative torsion angle is obtained. The maximum thrust stiffness value between the first thrust stiffness and the second thrust stiffness is taken as the minimum lateral thrust stiffness of the limiting device.
6. The conventional span continuous rigid frame beam end limiting design method as described in claim 5, characterized in that: Based on the minimum lateral thrust stiffness of the limiting device, the actual lateral thrust stiffness of the limiting device is determined, specifically including: Based on the minimum lateral thrust stiffness, the structural dimensions of the limiting device are initially determined; Based on the initially determined structural dimensions, the shear stiffness, bending stiffness, and thrust stiffness of the limiting device are obtained. The target lateral thrust stiffness is obtained based on shear stiffness, bending stiffness, and thrust stiffness. Based on the target lateral thrust stiffness and the minimum lateral thrust stiffness, the actual lateral thrust stiffness is determined.
7. The conventional span continuous rigid frame beam end limiting design method as described in claim 6, characterized in that: Based on the target lateral thrust stiffness and the minimum lateral thrust stiffness, the actual lateral thrust stiffness is determined, specifically including: Compare whether the target lateral thrust stiffness is greater than the minimum lateral thrust stiffness; If it is greater than that, the target lateral thrust stiffness will be taken as the actual lateral thrust stiffness. Otherwise, readjust the initially confirmed structural design dimensions until the target lateral thrust stiffness is greater than the minimum lateral thrust stiffness.
8. The conventional span continuous rigid frame beam end limiting design method as described in claim 7, characterized in that: Based on the actual lateral lateral stiffness of the limiting device, the actual relative displacement after the limiting device is installed at the beam end is obtained, specifically including: The actual horizontal relative displacement is obtained based on the lateral thrust stiffness, the actual lateral thrust stiffness, and the initial horizontal relative displacement. The actual relative torsion angle is obtained based on the lateral thrust stiffness, the beam end comprehensive coupling stiffness, the actual lateral thrust stiffness, the initial horizontal relative displacement, and the initial relative torsion angle. The actual relative displacement after the beam end is equipped with a limiting device includes the actual horizontal relative displacement and the actual relative torsional angle.
9. The conventional span continuous rigid frame beam end limiting design method as described in claim 1, characterized in that: Based on the allowable relative displacement and the actual relative displacement, determine whether the actual lateral thrust stiffness meets the design requirements, specifically including: Compare whether the allowable relative displacement is greater than the actual relative displacement; If it is greater than that, then the actual lateral thrust stiffness is confirmed to meet the design requirements. Otherwise, the actual lateral thrust stiffness should be readjusted.
10. The conventional span continuous rigid frame beam end limiting design method as described in claim 5, characterized in that: Verifying the strength of the limiting device specifically includes: The internal forces of the limiting device are obtained based on the lateral thrust stiffness and initial relative displacement. The strength of the limiting device is verified based on the internal force of the limiting device.