A prestress equivalent treatment method for a curved box girder bridge
By establishing a prestressed equivalent treatment method for curved box girder bridges, the problem of the spatial stress characteristics of curved box girder bridges not being considered in the design was solved. This method simplifies the simulation and provides a theoretical basis for the prestressing effect, supports the design, and reduces the occurrence of defects.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUNAN ENG POLYTECHNIC
- Filing Date
- 2026-03-10
- Publication Date
- 2026-06-05
AI Technical Summary
In the design process of curved box girder bridges, existing technologies have failed to effectively consider their spatial stress characteristics, resulting in defects such as support detachment, lateral displacement and tilting. Furthermore, the analysis of prestressing effects is complex and difficult to apply to displacement theory.
By establishing a prestressed equivalent treatment method for curved box girder bridges, including the calculation of equilibrium differential equations, prestressed initial internal force equations, and equivalent loads, and by reasonably simplifying the bending-torsional coupling characteristics, the prestressed equivalent loads are obtained.
The simplified prestressing effect can accurately simulate the prestressing effect of curved box girder bridges, providing a theoretical basis, facilitating bridge design, and reducing the occurrence of defects.
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Figure CN122154036A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of bridge design technology, specifically a prestressing equivalent treatment method for curved box girder bridges. Background Technology
[0002] Compared with orthogonal straight bridges, curved box girder bridges exhibit distinct spatial stress characteristics. Failure to fully consider these spatial stress characteristics can lead to defects such as support detachment and lateral displacement during use, and even serious accidents such as tilting.
[0003] Applying prestress is an effective method to increase the span capacity of bridges, improve structural stiffness, and reduce structural dimensions. Due to bending-torsional coupling, the prestressing effect applied to curved beams is also bending-torsional coupled, making the analysis of the prestressing effect much more complex than that for straight bridges. In particular, when the center angle of the curved beam increases, the characteristics of the bending-torsional coupling stress of the curved beam under the prestressing effect become more significant, which greatly increases the difficulty of analysis.
[0004] Therefore, in order to make the prestressing effect applicable to the displacement theory related to curved box girder bridges when designing bridges, the prestressing effect needs to be treated as an equivalent load and simplified accordingly. Summary of the Invention
[0005] The purpose of this application is to provide a prestressing equivalent treatment method for curved box girder bridges to solve the technical problems mentioned in the background, help to clarify the mechanism of prestressing effect in curved box girder bridges, and thus provide a corresponding theoretical basis for the design of curved box girder bridges.
[0006] To achieve the above objectives, this application discloses the following technical solution: a prestressing equivalent treatment method for curved box girder bridges, the method comprising the following steps: Step S1 - Based on the force balance at the micro-end of the curved box girder bridge, obtain the equilibrium differential equation of the curved box girder bridge under the action of prestressing load; Step S2 - Obtain the initial internal force equation of the prestressed box girder bridge based on the equilibrium of internal and external forces on the cross section; Step S3 - Substitute the prestressed initial internal force equation into the equilibrium differential equation, and after simplification, obtain the prestressed equivalent load of the curved box girder bridge. Step S4 - Process the equivalent load of the prestressing effect and make appropriate simplifications.
[0007] Preferably, in step S1, the equilibrium differential equation is specifically: in, Let be the first derivative of the shear force at the vertically upward end section of the curved beam with respect to the rotation angle. This represents the uniformly distributed force of the vertical upward prestressing on the curved beam. Let be the radius of curvature of the curved beam. Let be the first derivative of the bending moment at the radial upper end section of the curved beam with respect to the rotation angle. The torque at the end section, Let be the uniformly distributed torque of the radial prestress of the curved beam. Let be the first derivative of the torque at the end section with respect to the rotation angle. Let be the bending moment at the radial upper end section of the curved beam. Let be the uniformly distributed torque of the tangential prestress of the curved beam. Let be the first derivative of the shear force at the radial upper end section of the curved beam with respect to the rotation angle. The axial force at the end section, This represents the uniformly distributed prestressing force in the radial direction of the curved beam. Let be the first derivative of the axial force at the end section with respect to the rotation angle. Let be the shear force at the radial upper end section of the curved beam. This represents the uniformly distributed prestressing force in the tangential direction of the curved beam. Let be the first derivative of the bending moment at the vertically upward end section of the curved beam with respect to the rotation angle. This represents the uniformly distributed torque of the vertical upward prestress of the curved beam.
[0008] Preferably, in step S2, the initial internal force equation of the prestressed force is: in, The resultant force of the prestress on the end section, The transverse coordinates of the prestressed steel strands on the end section are: The vertical coordinates of the prestressed steel strands on the end section are: The first derivative of the transverse coordinate of the prestressed steel strand on the end section with respect to the rotation angle. It is the first derivative of the vertical coordinate of the prestressed steel strand on the end section with respect to the rotation angle.
[0009] Preferably, in step S3, the prestressed equivalent load obtained is: in, Let be the second derivative of the transverse coordinate of the prestressed steel strand on the end section with respect to the rotation angle. It is the second derivative of the vertical coordinate of the prestressed steel strand on the end section with respect to the rotation angle.
[0010] Preferably, in step S4, the simplified equivalent load of the prestressing effect is: The simplified conditions are: the prestressed steel strands are arranged asymmetrically, and the change of the vertical coordinate of the prestressed steel strands along the longitudinal direction is not considered.
[0011] Beneficial Effects: The prestressing equivalent treatment method for curved box girder bridges proposed in this application, by simplifying the prestressing effect to take into account the bending-torsional coupling characteristics, can reasonably and accurately simulate the prestressing effect of curved box girder bridges. Furthermore, to ensure that the prestressing effect is applicable to the relevant displacement theories of curved box girder bridges, the prestressing effect is treated as an equivalent load and reasonably simplified. This method helps to clarify the mechanism of the prestressing effect in curved box girder bridges, thus facilitating the subsequent design of curved box girder bridges. Attached Figure Description
[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the 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.
[0013] Figure 1 A schematic diagram of the equilibrium of equivalent load and internal force on the micro-end of a curved beam provided in an embodiment of this application; Figure 2 A schematic diagram of the prestress components on the cross section provided for embodiments of this application; Figure 3 This is a simplified diagram of the prestressing equivalent treatment provided in the embodiments of this application. Detailed Implementation
[0014] The technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0015] In this document, the term "comprising" is intended to cover a 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 limitation, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0016] This embodiment provides a method for equivalent prestressing treatment of curved box girder bridges, which includes the following steps: Step S1 - Based on the force balance at the micro-end of the curved box girder bridge, obtain the equilibrium differential equation of the curved box girder bridge under the action of prestressing load; Step S2 - Obtain the initial internal force equation of the prestressed box girder bridge based on the equilibrium of internal and external forces on the cross section; Step S3 - Substitute the prestressed initial internal force equation into the equilibrium differential equation, and after simplification, obtain the prestressed equivalent load of the curved box girder bridge. Step S4 - Process the equivalent load of the prestressing effect and make appropriate simplifications.
[0017] Furthermore, such as Figure 1 As shown, the curved girder segment is subjected to prestressed equivalent uniformly distributed loads in six directions, and there are internal forces in six directions at each end of the cross-section. Based on the force equilibrium at the ends of the curved box girder bridge, the equilibrium differential equation of the curved girder under prestressed load can be obtained: In the formula, Let be the first derivative of the shear force at the vertically upward end section of the curved beam with respect to the rotation angle. This represents the uniformly distributed force of the vertical upward prestressing on the curved beam. Let be the radius of curvature of the curved beam. Let be the first derivative of the bending moment at the radial upper end section of the curved beam with respect to the rotation angle. The torque at the end section, Let be the uniformly distributed torque of the radial prestress of the curved beam. Let be the first derivative of the torque at the end section with respect to the rotation angle. Let be the bending moment at the radial upper end section of the curved beam. Let be the uniformly distributed torque of the tangential prestress of the curved beam. Let be the first derivative of the shear force at the radial upper end section of the curved beam with respect to the rotation angle. The axial force at the end section, This represents the uniformly distributed prestressing force in the radial direction of the curved beam. Let be the first derivative of the axial force at the end section with respect to the rotation angle. Let be the shear force at the radial upper end section of the curved beam. This represents the uniformly distributed prestressing force in the tangential direction of the curved beam. Let be the first derivative of the bending moment at the vertically upward end section of the curved beam with respect to the rotation angle. This represents the uniformly distributed torque of the vertical upward prestress of the curved beam.
[0018] After geometric transformation, the components of the prestressed resultant force F on the end section in the vertical, radial, and tangential directions are respectively... , ,and ,like Figure 2 As shown. Wherein: , , ; For a prestressed cable arc length micro-segment, under normal circumstances Based on the equilibrium of internal and external forces on the cross section, the initial internal force equation for the prestressed curved box girder bridge can be obtained as follows: In the formula, The resultant force of the prestress on the end section, The transverse coordinates of the prestressed steel strands on the end section are: The vertical coordinates of the prestressed steel strands on the end section are: The first derivative of the transverse coordinate of the prestressed steel strand on the end section with respect to the rotation angle. It is the first derivative of the vertical coordinate of the prestressed steel strand on the end section with respect to the rotation angle.
[0019] Furthermore, substituting the obtained initial prestressed internal force equations into the equilibrium differential equations and simplifying, we can obtain the equivalent prestressed load for the curved box girder bridge as follows: In the formula, Let be the second derivative of the transverse coordinate of the prestressed steel strand on the end section with respect to the rotation angle. It is the second derivative of the vertical coordinate of the prestressed steel strand on the end section with respect to the rotation angle.
[0020] It can be seen that the prestress acting on the curved beam not only applies end forces in six directions to the beam ends, but also applies uniformly distributed forces in six directions to the beam body. The concentrated end forces and the uniformly distributed forces on the beam body balance the forces on the entire beam segment.
[0021] Once the prestressed steel strands are determined, their h value is known to be constant. Considering the influence of some complex factors during construction and the needs of some special situations, the prestressed steel strands generally cannot be completely symmetrical; therefore, the prestressed steel strands are arranged asymmetrically. To simplify the calculation, the variation of the vertical coordinate z of the prestressed steel strands along the longitudinal direction is not considered. Figure 3 As shown. After the above simplification process, the equivalent load of the prestressing effect is: Therefore, the equivalent prestressed load can be simplified to a radially distributed force and a uniformly distributed torque along the entire length of the bridge, which takes into account the characteristic that the prestressed effect applied to it is also a bending-torsional coupling.
[0022] Finally, it should be noted that the above description is only a preferred embodiment of this application and is not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.
Claims
1. A method for equivalent prestressing treatment of a curved box girder bridge, characterized in that, The method includes the following steps: Step S1 - Based on the force balance at the micro-end of the curved box girder bridge, obtain the equilibrium differential equation of the curved box girder bridge under the action of prestressed load; Step S2 - Obtain the initial internal force equation of the prestressed box girder bridge based on the equilibrium of internal and external forces on the cross section; Step S3 - Substitute the prestressed initial internal force equation into the equilibrium differential equation, and after simplification, obtain the prestressed equivalent load of the curved box girder bridge. Step S4 - Process the equivalent load of the prestressing effect and make appropriate simplifications.
2. The prestressing equivalent treatment method for curved box girder bridges according to claim 1, characterized in that, In step S1, the equilibrium differential equation is specifically: in, Let be the first derivative of the shear force at the vertically upward end section of the curved beam with respect to the rotation angle. This represents the uniformly distributed force of the vertical upward prestressing on the curved beam. Let be the radius of curvature of the curved beam. Let be the first derivative of the bending moment at the radial upper end section of the curved beam with respect to the rotation angle. The torque at the end section, Let be the uniformly distributed torque of the radial prestress of the curved beam. Let be the first derivative of the torque at the end section with respect to the rotation angle. Let be the bending moment at the radial upper end section of the curved beam. Let be the uniformly distributed torque of the tangential prestress of the curved beam. Let be the first derivative of the shear force at the radial upper end section of the curved beam with respect to the rotation angle. The axial force at the end section, This represents the uniformly distributed prestressing force in the radial direction of the curved beam. Let be the first derivative of the axial force at the end section with respect to the rotation angle. Let be the shear force at the radial upper end section of the curved beam. This represents the uniformly distributed prestressing force in the tangential direction of the curved beam. Let be the first derivative of the bending moment at the vertically upward end section of the curved beam with respect to the rotation angle. This represents the uniformly distributed torque of the vertical upward prestress of the curved beam.
3. The prestressing equivalent treatment method for curved box girder bridges according to claim 2, characterized in that, In step S2, the initial internal force equation for prestress is: in, The resultant force of the prestress on the end section, The transverse coordinates of the prestressed steel strands on the end section are: The vertical coordinates of the prestressed steel strands on the end section are: The first derivative of the transverse coordinate of the prestressed steel strand on the end section with respect to the rotation angle. It is the first derivative of the vertical coordinate of the prestressed steel strand on the end section with respect to the rotation angle.
4. The prestressing equivalent treatment method for curved box girder bridges according to claim 3, characterized in that, In step S3, the obtained prestressed equivalent load is: in, Let be the second derivative of the transverse coordinate of the prestressed steel strand on the end section with respect to the rotation angle. It is the second derivative of the vertical coordinate of the prestressed steel strand on the end section with respect to the rotation angle.
5. The prestressing equivalent treatment method for curved box girder bridges according to claim 4, characterized in that, In step S4, the simplified equivalent load of the prestressing effect is: The simplified conditions are: the prestressed steel strands are arranged asymmetrically, and the change of the vertical coordinate of the prestressed steel strands along the longitudinal direction is not considered.