Method and system for determining bearing capacity of prefabricated assembled bridge pier under compression-bending-shearing-torsion action

Abstract

The present application relates to the technical field of bridge engineering, in particular to a method and system for determining the bearing capacity of a prefabricated and assembled bridge pier under compression-bending-shear-torsion action, comprising determining the stress failure model and analysis assumption conditions of the prefabricated and assembled bridge pier, and then establishing the limit axial force expression and shear force balance equation; the limit axial force expression, shear force balance equation, bending moment equation and torsion equation are derived to obtain the unified analysis equation of the prefabricated and assembled bridge pier; the joint torsional bearing capacity calculation formula is constructed based on the shear bearing capacity data and joint stress conditions; the peak load of different prefabricated and assembled bridge piers is calculated and compared with the test according to the unified analysis equation of the prefabricated and assembled bridge pier and the joint torsional bearing capacity calculation formula. The present application comprehensively considers the combined action of compression, bending moment, shear force and torsion, can more accurately reflect the stress condition of the prefabricated and assembled bridge pier, and realizes the accurate prediction of the peak bearing capacity and peak torsion of the prefabricated and assembled bridge pier under compression-bending-shear-torsion load action.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, specifically to a method and system for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion. Background Technology

[0002] In the field of bridge engineering, precast bridge piers effectively reduce on-site construction time and traffic disruption, improving project progress and quality. During actual operation, bridge structures simultaneously bear multiple loads, including compression, bending moment, shear force, and torque. If the bearing capacity of the piers under these combined loads is insufficient, it can lead to cracks, excessive deformation, or even failure, severely impacting the safety and normal use of the bridge structure. Therefore, accurately determining the bearing capacity of precast bridge piers under compression, bending, shear, and torsion is crucial for ensuring the safety and reliability of bridge structures.

[0003] Currently, most methods for analyzing the bearing capacity of bridge piers are based on single load conditions. There is little research on the bearing capacity of precast bridge piers under combined loads of compression, bending, shear and torsion. Single load research methods, such as those that only consider the bearing capacity of bridge piers under axial pressure, bending moment or shear force, are difficult to apply directly to combined load conditions.

[0004] The lack of a unified and comprehensive theoretical system for the stress analysis of precast bridge piers under combined compression, bending, shear, and torsion loads leads to significant discrepancies in calculation results, making it difficult to accurately reflect the actual stress conditions of the piers. Existing calculation methods often employ simplification when considering multiple loads, neglecting the interactions and coupling effects between loads, resulting in large deviations between calculation results and actual conditions. Furthermore, the lack of sufficient experimental data to verify and correct theoretical models and calculation methods makes it difficult to directly apply theoretical research results to practical engineering projects.

[0005] Therefore, a method and system for determining the bearing capacity of precast bridge piers under bending, shear and torsion is needed. This provides a scientific and accurate analytical method for assessing the bearing capacity of precast bridge piers under complex loads, which will help improve the design level and safety of bridge structures and promote the development of bridge engineering technology. Summary of the Invention

[0006] To address the shortcomings of existing methods and the inadequacies of practical applications, this study aims to achieve unified analysis of precast bridge piers, accurately predict the peak bearing capacity and torque of precast bridge piers under compression, bending, shear, and torsion loads, provide a scientific and accurate method for assessing the bearing capacity of precast bridge piers under complex loads, improve the level and safety of bridge structural design, and promote the development of bridge engineering technology. In a first aspect, this invention provides a method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion loads. The method includes the following steps: determining the stress-failure model and analytical assumptions of the precast assembled bridge pier; establishing the ultimate axial force expression and shear force equilibrium equation of the precast assembled bridge pier based on the stress-failure model and analytical assumptions; constructing the bending moment equation and torque equation of the precast assembled bridge pier; deriving the ultimate axial force expression, the shear force equilibrium equation, the bending moment equation, and the torque equation to obtain a unified analytical equation for the precast assembled bridge pier; acquiring the shear bearing capacity data and joint stress conditions of the precast assembled bridge pier; constructing a joint torsional bearing capacity calculation formula based on the shear bearing capacity data and the joint stress conditions; and performing peak load calculations and experimental comparisons on different precast assembled bridge piers based on the unified analytical equation and the joint torsional bearing capacity calculation formula to predict the peak bearing capacity and peak torque of the precast assembled bridge pier under compression, bending, shear, and torsion loads.

[0007] This invention predicts peak loads under different load combinations by using unified analytical equations and joint torsional bearing capacity calculation formulas, which helps to identify problems in the design and use of bridge piers and avoid bridge collapse accidents caused by pier failure.

[0008] Optionally, determining the stress-failure model and analytical assumptions for the precast assembled bridge pier includes: conducting experimental analysis on the crack distribution and mechanical state of the precast assembled bridge pier and obtaining experimental observation results; determining the stress-failure model of the precast assembled bridge pier based on the experimental observation results; and setting analytical assumptions for the precast assembled bridge pier based on the stress-failure model and the experimental observation results. These analytical assumptions include: concrete only bearing compressive stress; stirrups intersecting the spiral crack only bearing tensile stress and reaching a yield state; local unbonded prestressing tendons reaching yield under compression-bending-shear and compression-bending-shear-torsion loads; prestress magnitude remaining constant under compression-torsion loads; and the resultant force in the compression zone acting at the centroid of the compression zone. point.

[0009] The experimental observation results of this invention can intuitively show the failure phenomenon and characteristics of bridge piers during actual stress, providing information for the failure mechanism of prefabricated bridge piers and providing data support for the establishment of mechanical equations.

[0010] Optionally, establishing the ultimate axial force expression and shear force equilibrium equation of the precast assembled bridge pier based on the stress failure model and the analysis assumptions includes: deriving the ultimate axial force expression and shear force equilibrium equation of the precast segmental assembled bridge pier under compression-bending-shear-torsion loads based on the stress failure model and the analysis assumptions.

[0011] The expression for the limiting axial force satisfies the following relationship:

[0012] ,

[0013] in, To test the ultimate compressive strength of precast and assembled bridge piers, The resultant force provided to the concrete in the compression zone For the magnitude of the stress on the tension prestressing tendon, This refers to the force of a single prestressed tendon in the compression zone.

[0014] The limit axial force expression established in this invention provides a quantitative technique for the standardization of prefabricated assembled bridge piers.

[0015] Optionally, the shear force equilibrium equation satisfies the following relationship:

[0016] ,

[0017] in, To assess the shear bearing capacity of precast and assembled bridge piers, For the stirrups to bear the force, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups.

[0018] The shear equilibrium equation of this invention provides an important theoretical tool for the mechanical analysis of prefabricated bridge piers, which helps to conduct a more systematic and comprehensive analysis of the piers under various load combinations.

[0019] Optionally, the bending moment equation and torque equation for constructing the precast bridge pier include: the precast bridge pier about the centroid of the compression zone under compression-bending-shear-torsional loads. The bending moment equation and torque equation at a point satisfy the following relationships:

[0020] ,

[0021] in, To improve the bending capacity of precast and assembled bridge piers, For the force of the prestressed tendons in the compression zone, For the prestressed tendons in the compression zone to Vertical distance between points For the magnitude of the stress on the tension prestressing tendon, For the prestressed tendons in the tension zone to Vertical distance between points For the tensile strength of concrete, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups; ,

[0022] in, To assess the torsional bearing capacity of precast and assembled bridge piers, For the stirrups to bear the force, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The effective width of the cross section, The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups.

[0023] The two equations in this invention work together to comprehensively and accurately describe the mechanical response of bridge piers under different load combinations, providing a foundation for further analysis and making the analysis process of prefabricated bridge piers more systematic and scientific.

[0024] Optionally, the derivation of the ultimate axial force expression, the shear force balance equation, the bending moment equation, and the torque equation to obtain the unified analysis equation for prefabricated assembled bridge piers includes: substituting the ultimate axial force expression, the shear force balance equation, and the torque equation into the bending moment equation to derive the unified analysis equation for prefabricated assembled bridge piers;

[0025] The unified analytical equation for the prefabricated assembled bridge piers satisfies the following relationship:

[0026] ,

[0027] in, To assess the torsional bearing capacity of precast and assembled bridge piers, This refers to the peak torque of precast segmental bridge piers under pure torsional load. To assess the shear bearing capacity of precast and assembled bridge piers, The shear force of precast segmental bridge piers under pure shear load. To test the ultimate compressive strength of precast and assembled bridge piers, The axial force of the precast segmental bridge pier under pure compressive load. To improve the bending capacity of precast and assembled bridge piers, The bending moment of a precast segmental bridge pier under pure bending load.

[0028] The unified analytical equation of this invention integrates the bearing capacity relationship of prefabricated bridge piers under various loads such as compression, bending, shear and torsion into one equation, clearly showing the mutual influence and constraint relationship between different load components (torque, shear force, axial force and bending moment), which helps to deeply understand the mechanical behavior of bridge piers under complex stress conditions.

[0029] Optionally, obtaining the shear bearing capacity data and joint stress conditions of the precast piers includes: introducing a method for calculating the torsional bearing capacity of the precast pier joints under compression-bending-shear-torsion loads; obtaining the shear bearing capacity data of the precast piers based on the torsional bearing capacity calculation method; drawing a torsional bearing capacity analysis diagram of the precast pier joints; and analyzing the joint stress conditions of the precast piers based on the torsional bearing capacity analysis diagram.

[0030] The torsional bearing capacity calculation method of this invention can effectively analyze the mechanical behavior of joints in complex load environments, help to fully understand the working mechanism of joints under different stress conditions, and improve the mechanical theory system of precast bridge pier joints.

[0031] Optionally, the step of constructing the joint torsional bearing capacity calculation formula based on the shear bearing capacity data and the joint stress condition includes:

[0032] The formula for calculating the torsional bearing capacity of the joint satisfies the following relationship:

[0033] ,

[0034] in, For the torsional bearing capacity of the joint, This represents the ultimate shear stress of the joint. The formula in this invention establishes a clear relationship between the torsional bearing capacity of the joint and the ultimate shear stress and the torsional plastic modulus of the section, providing a clear quantitative relationship for the mechanical behavior of the joint under torsion.

[0035] Optionally, the step of calculating and comparing peak loads of different prefabricated piers based on the unified analysis equation for prefabricated piers and the calculation formula for the torsional bearing capacity of joints, to achieve accurate prediction of the peak bearing capacity and peak torque of prefabricated piers under compression-bending-shear-torsion loads, includes: analyzing the interaction between prefabricated piers under fixed axial force and compression-bending-shear-torsion loads using the unified analysis equation for prefabricated piers; analyzing the analysis results of the torsional bearing capacity of joints of prefabricated piers using the calculation formula for the torsional bearing capacity of joints; obtaining the peak loads of different prefabricated piers by combining the interaction and the analysis results of the torsional bearing capacity of joints; introducing the test results of prefabricated piers; comparing and analyzing the test results and the peak loads to obtain the comparison analysis results; and accurately predicting the peak bearing capacity and peak torque of prefabricated piers under compression-bending-shear-torsion loads based on the comparison analysis results.

[0036] This invention can accurately predict the peak bearing capacity and peak torque of prefabricated bridge piers under compression, bending, shear and torsion loads, further ensuring that the bridge piers have sufficient bearing capacity and good deformation performance under various complex load conditions, thus improving the safety and reliability of the structure.

[0037] Secondly, the present invention also provides a system for determining the bearing capacity of precast assembled bridge piers under bending, shear, and torsion loads. This system can efficiently execute the method for determining the bearing capacity of precast assembled bridge piers under bending, shear, and torsion loads provided by the present invention. The system includes an input device, a processor, an output device, and a memory, wherein the input device, processor, output device, and memory are interconnected. The memory includes a computer-readable storage medium as described in the first aspect of the present invention, and is used to store a computer program. The computer program includes program instructions, and the processor is configured to call the program instructions. The system for determining the bearing capacity of precast assembled bridge piers under bending, shear, and torsion loads provided by the present invention has a compact structure, strong applicability, and greatly improves operating efficiency. Attached Figure Description

[0038] Figure 1 This is a flowchart of the method for determining the bearing capacity of prefabricated bridge piers under bending, shear and torsion loads according to the present invention.

[0039] Figure 2 This is a schematic diagram of the stress failure model and stress state under compression, bending, shear and torsion loads of the present invention;

[0040] Figure 3 This is a diagram showing the torsional bearing capacity analysis of the joints of the prefabricated assembled bridge piers of the present invention.

[0041] Figure 4 This is a diagram showing the relationship between bending, shear, and torsional loads on the prefabricated segmental piers of this invention.

[0042] Figure 5This is a structural schematic diagram of the system for determining the bearing capacity of prefabricated assembled bridge piers under bending, shearing and torsion conditions according to the present invention. Detailed Implementation

[0043] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0044] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0045] Please see Figure 1 To effectively assess the load-bearing capacity of precast bridge piers under complex load conditions, improve the rationality and safety of bridge structural design, and provide technical support for the continuous development of bridge engineering technology, this invention provides a method for determining the load-bearing capacity of precast bridge piers under compression, bending, shear, and torsion. The method includes the following steps:

[0046] Based on existing theoretical research and experimental analysis data, it is known that under combined compression, bending, shear, and torsion loads, the peak strength of a precast bridge pier depends on the smaller of the strength provided by the pier body and the joint. That is, when slippage or torsion occurs at the joint of a precast bridge pier, the lateral force and torque possessed by the pier itself will inevitably exceed the frictional force and torque generated at the joint; conversely, if the frictional force and torque at the joint are greater than the lateral force and torque of the pier, then the pier will not experience joint slippage or torsion. Next, the method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion loads of this invention will describe the calculation methods for the peak strength of the pier and the joint.

[0047] S1. Determine the stress-failure model and analysis assumptions for the precast bridge piers. Based on the above stress-failure model and analysis assumptions, establish the ultimate axial force expression and shear force equilibrium equation for the precast bridge piers. The implementation steps and specific contents are as follows:

[0048] First, determine the stress failure model and analysis assumptions for the precast bridge piers.

[0049] This embodiment conducts a simulation test on prefabricated assembled bridge piers, and performs an in-depth analysis of their crack distribution and mechanical state. Simultaneously, relevant data is recorded and organized during the test to obtain comprehensive and accurate experimental observation results.

[0050] Because the stress state of precast bridge piers under compression, bending, shear, and torsion loads is extremely complex, observations of the crack distribution and mechanical state of the piers during the experiment reveal that when the piers are under peak load, a specific stress-failure model will form, such as... Figure 2 As shown in (a), where T is torque, N is axial force, M is bending moment, and V is shear force, it intuitively presents the correspondence between the stress failure model and the stress state under compression, bending, shear and torsion loads, providing an intuitive and crucial reference for subsequent research.

[0051] Based on the above stress failure model Figure 2 Based on (a) and experimental observation results, reasonable analytical assumptions for prefabricated bridge piers should be set.

[0052] The following key analytical assumptions are set in this embodiment:

[0053] Concrete stress assumptions: Concrete is only subjected to compressive stress, and tensile stress or other stress conditions are not considered in subsequent analysis and calculation.

[0054] Stirrup stress assumptions: The stirrups intersecting the helical crack only bear tensile force and reach a yield state during the stress process. Meanwhile, for the sake of simplifying the analysis, the effect of longitudinal reinforcement within the segment is ignored.

[0055] The stress assumptions for prestressed tendons are as follows: under compression-bending-shear and compression-bending-shear-torsion loads, the local unbonded prestressed tendons reach the yield state; while under compression-torsion loads, the magnitude of the prestress remains unchanged.

[0056] Assumption of the resultant force in the compression zone: The point of application of the resultant force in the compression zone is located at the centroid of the compression zone. This point is used to determine the location of the resultant force in the compression zone, which facilitates subsequent mechanical analysis.

[0057] In addition, a schematic diagram of the stress state of precast assembled bridge piers under compression, bending, shear, and torsion loads is provided. Figure 2 From (b) in the diagram, we can see that T is the torque, N is the axial force, M is the bending moment, and V is the shear force. The width of the bridge pier cross section. For the magnitude of the stress on the tension prestressing tendon, The angle between the cracks on the two surfaces parallel to the loading direction and the direction along the pier height. The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. For the stirrups to bear the force, For the force of the prestressed tendons in the compression zone, Centroid of the pressure zone point, The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the cracks on the two surfaces parallel to the loading direction and the direction along the pier height. The resultant force provided to the concrete in the compression zone. Based on Figure 2 (a) and Figure 2 As shown in (b), the failure characteristics of the stress-induced failure model are manifested by the appearance of openings in the joints, and the diagonal cracks on the three surfaces of the pier forming a torsional failure surface. Furthermore, the angles between the cracks on the two surfaces parallel to the loading direction and the direction along the pier height are respectively... and The aforementioned features need to be fully considered in subsequent analysis and calculations.

[0058] Then, based on the stress failure model and analytical assumptions, the ultimate axial force expression and shear force equilibrium equation of the prefabricated assembled bridge pier are established.

[0059] By analyzing the stress-failure model and combining the analytical assumptions, the expression for the ultimate axial force of precast segmental bridge piers under compression, bending, shear, and torsion loads is derived. This expression clearly reflects the intrinsic relationship between the ultimate axial force and various related mechanical parameters.

[0060] The above expression for the limiting axial force satisfies the following relationship:

[0061] ,

[0062] in, To test the ultimate compressive strength of precast and assembled bridge piers, The resultant force provided to the concrete in the compression zone The magnitude of the stress on the tension prestressing tendon This refers to the force exerted by the prestressing tendons in the compression zone.

[0063] The ultimate compressive strength of precast bridge piers is an important indicator for measuring the pier's ability to withstand pressure under ultimate conditions; the resultant force provided by the concrete in the compression zone reflects the contribution of the concrete to the overall bearing capacity of the pier under compression; the force of a single prestressing tendon in the compression zone highlights the role played by the prestressing tendon in the compression zone.

[0064] Based on the stress failure model and analytical assumptions, the shear equilibrium equation of precast segmental piers under compression, bending, shear and torsion loads is further derived. This equation is of great significance for analyzing the equilibrium state of piers under shear force and evaluating their shear bearing capacity.

[0065] The above shear force equilibrium equations satisfy the following relationship:

[0066] ,

[0067] in, To assess the shear bearing capacity of precast and assembled bridge piers, For the stirrups to bear the force, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups.

[0068] The shear bearing capacity of precast bridge piers is an important parameter for measuring the pier's ability to resist shear force; the stress on the stirrups reflects the force borne by the stirrups in resisting shear force; the vertical distance is closely related to the distribution and stress state of cracks; the included angle affects the way cracks affect the mechanical properties of the bridge pier; the stirrup spacing determines the distribution density of the stirrups in the bridge pier, which has an important impact on the shear resistance of the bridge pier.

[0069] S2. Construct the bending moment and torque equations for precast bridge piers, and derive the expressions for ultimate axial force, shear force equilibrium, bending moment, and torque equations to obtain a unified analysis equation for precast bridge piers. The specific steps and implementation details are as follows:

[0070] First, construct the bending moment equation and torque equation for the prefabricated bridge piers.

[0071] To explore the mechanical properties of precast bridge piers under compression, bending, shear, and torsion loads, this embodiment constructs bending moment equations and torque equations. These two equations can quantitatively describe the mechanical response of bridge piers under complex loads, providing a solid theoretical basis for subsequent structural design and safety assessment.

[0072] Under the combined action of compression, bending, shear, and torsion loads, the precast and assembled bridge piers revolve around the centroid of the compression zone. A bending moment will be generated at a point. By performing a stress analysis on the bridge pier and combining relevant principles of mechanics of materials and structural mechanics, the bending moment equation is derived to satisfy the following relationship:

[0073] ,

[0074] in, To improve the bending capacity of precast and assembled bridge piers, For the force of a single prestressed tendon in the compression zone, For the prestressed tendons in the compression zone to Vertical distance between points For the magnitude of the stress on the tension prestressing tendon, For the prestressed tendons in the tension zone to Vertical distance between points For the stirrups to bear the force, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the cracks on the two surfaces parallel to the loading direction and the direction along the pier height. The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the cracks on the two surfaces parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups;

[0075] Similarly, under the action of compression-bending-shear-torsion loads, the precast assembled bridge piers are positioned around the centroid of the compression zone. A point will also generate torque. By analyzing the mechanism of torque generation and combining relevant mechanical theories, the torque equation is derived to satisfy the following relationship:

[0076] ,

[0077] in, To assess the torsional bearing capacity of precast and assembled bridge piers, For the stirrups to bear the force, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The effective width of the cross section, The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups.

[0078] Then, the expressions for the ultimate axial force, shear force balance equation, bending moment equation, and torque equation are derived to obtain the unified analysis equation for prefabricated assembled bridge piers.

[0079] After deriving the expressions for the ultimate axial force, shear force equilibrium equation, bending moment equation, and torque equation, in order to comprehensively analyze the mechanical performance of precast assembled bridge piers under complex loads, it is necessary to further derive a unified analysis equation for precast assembled bridge piers. This unified analysis equation can integrate the responses of bridge piers under different load components, providing a more comprehensive reference for structural design and safety assessment.

[0080] In this embodiment, the expression for the ultimate axial force, the shear force balance equation, and the torque equation are substituted into the bending moment equation. Through mathematical calculations and simplification, a unified analysis equation for prefabricated assembled bridge piers that can simultaneously consider the mutual influence of bending moment, torque, shear force, and axial force is obtained. The above process is based on the mechanical properties of materials and structures under multiaxial stress in structural mechanics. It is assumed that there are certain mutual constraints between the bearing capacities of the bridge piers under different load components, and that the overall bearing capacity satisfies certain energy conservation or strength criteria.

[0081] The unified analytical equation for the above prefabricated bridge piers satisfies the following relationship:

[0082] ,

[0083] in, To assess the torsional bearing capacity of precast and assembled bridge piers, This refers to the peak torque of precast segmental bridge piers under pure torsional load. To assess the shear bearing capacity of precast and assembled bridge piers, The shear force of precast segmental bridge piers under pure shear load. To test the ultimate compressive strength of precast and assembled bridge piers, The axial force of precast segmental bridge piers under pure compressive load. To improve the bending capacity of precast and assembled bridge piers, The bending moment of a precast segmental bridge pier under pure bending load.

[0084] Based on the above implementation details, it can be seen that... , , and The peak torque, shear force, axial force, and bending moment of precast segmental bridge piers under pure torsion, pure shear, pure compression, and pure bending loads are calculated using the following relationships:

[0085] I. Peak Torque

[0086] ,

[0087] in, This refers to the peak torque of precast segmental bridge piers under pure torsional load. For the stirrups to bear the force, The effective width of the cross section, The resultant force provided to the concrete in the compression zone For the magnitude of the stress on the tension prestressing tendon, The vertical distance from the prestressed tendon in the compression zone to point C. For the prestressed tendons in the tension zone to Vertical distance between points This refers to the spacing between the stirrups.

[0088] II. Peak Shear Force

[0089] ,

[0090] in, The shear force of precast segmental bridge piers under pure shear load. For the stirrups to bear the force, The resultant force provided to the concrete in the compression zone For the magnitude of the stress on the tension prestressing tendon, For the prestressed tendons in the compression zone to The vertical distance between the points is the distance from the prestressed tendon in the tension zone to the... Vertical distance between points This refers to the spacing between the stirrups.

[0091] III. Peak Axial Force

[0092] ,

[0093] in, The axial force of precast segmental bridge piers under pure compressive load. The resultant force provided to the concrete in the compression zone For the magnitude of the stress on the tension prestressing tendon, For the prestressed tendons in the compression zone to Vertical distance between points The vertical distance from the prestressed tendon in the tension zone to point C. This refers to the spacing between the stirrups.

[0094] IV. Peak bending moment

[0095] ,

[0096] in, The bending moment of precast segmental bridge piers under pure bending load. The resultant force provided to the concrete in the compression zone For the prestressed tendons in the tension zone to bear the force, For the prestressed tendons in the compression zone to Vertical distance between points For the prestressed tendons in the tension zone to The perpendicular distance between points.

[0097] Through the above derivation and calculation, a unified analytical equation for prefabricated bridge piers and a calculation method for each peak parameter can be obtained, providing strong theoretical support for comprehensively evaluating the mechanical performance of bridge piers under complex loads.

[0098] S3. Obtain the shear bearing capacity data and joint stress conditions of the precast assembled bridge piers. Based on the shear bearing capacity data and joint stress conditions, construct the calculation formula for the torsional bearing capacity of the joints. The specific steps and implementation details are as follows:

[0099] First, obtain the shear bearing capacity data and joint stress conditions of the precast bridge piers.

[0100] A method for calculating the torsional bearing capacity of precast bridge pier joints under compression, bending, shear and torsion loads is introduced, and then the shear bearing capacity data of precast assembled bridge piers are obtained based on the torsional bearing capacity calculation method.

[0101] The core logic of the torsional bearing capacity calculation method lies in the fact that, based on the theoretical results obtained from the torsional bearing capacity calculation, the shear bearing capacity data of prefabricated assembled bridge piers can be further derived. Through correlation derivation, the intrinsic relationship between torsional and shear bearing capacity can be established, providing comprehensive data support for subsequent analysis.

[0102] Draw a torsional bearing capacity analysis diagram of the joints of precast bridge piers, and analyze the stress situation of the joints of precast bridge piers based on the torsional bearing capacity analysis diagram.

[0103] To more intuitively and clearly demonstrate the torsional bearing capacity characteristics of precast bridge pier joints, a torsional bearing capacity analysis diagram of the joints is presented in this embodiment. Please refer to the following for details. Figure 3 Where V is shear force, T is torque, and N is axial force. This refers to the elongation of the prestressing tendons. The angle of rotation of the bridge pier around the column base. The resultant force of compressive stress in the concrete of the compression zone. The height of the tension zone, For the prestressing tendons in the tension zone, The area of ​​the prestressing tendons in the tension zone, The initial stress of the prestressing tendon. For the prestressing tendons in the compression zone, The area of ​​the prestressing tendons in the compression zone. Figure 3 It is helpful to intuitively present the variation law of the load-bearing capacity of the joint under different stress combinations.

[0104] Based on the analysis diagram of the torsional bearing capacity of the joint ( Figure 3 It can provide in-depth analysis of the stress conditions of the joints of prefabricated bridge piers, which is helpful in judging the stability and safety of the joints under different stress conditions. When the torque reaches a certain value, it indicates that there is a potential risk in the joint under that stress condition, and further optimization of the design or strengthening of the structural measures is required.

[0105] Through the above steps, we can obtain comprehensive and accurate shear bearing capacity data of precast bridge piers, and conduct in-depth analysis of the stress situation of joints, providing a reliable theoretical basis and practical guidance for the subsequent structural design and safety assessment of precast bridge piers.

[0106] After obtaining the shear bearing capacity data of the precast and assembled bridge piers and analyzing the stress conditions of the joints, a formula for calculating the torsional bearing capacity of the joints is constructed based on the above stress characteristics, shear bearing capacity data and joint stress conditions.

[0107] The above formula for calculating the torsional bearing capacity of joints satisfies the following relationship:

[0108] ,

[0109] in, For the torsional bearing capacity of the joint, This represents the ultimate shear stress of the joint. The cross-sectional torsional plastic modulus of the joint.

[0110] Joint torsional bearing capacity is a key indicator for measuring a joint's ability to resist torque; joint ultimate shear stress reflects the shear strength of the joint material under ultimate conditions; the torsional plastic modulus of a joint section is related to the geometry and size of the joint and reflects the section's ability to resist torsional deformation.

[0111] This embodiment further analyzes the calculation formulas for ultimate shear stress under different conditions.

[0112] When the torsional bearing capacity of the joint is mainly provided by the frictional force of the compression zone, the ultimate shear stress satisfies the following calculation formula:

[0113] ,

[0114] in, This represents the ultimate shear stress of the joint. The coefficient of friction, The average compressive stress in the compression zone of the concrete is given. The friction coefficient mentioned above is related to factors such as the roughness of the joint surface and the material properties; the average compressive stress in the compression zone of the concrete reflects the stress level of the concrete under compression.

[0115] For joints with shear keys, considering the combined effect of the shear resistance of the shear keys and friction, the formula for calculating the ultimate shear stress is as follows:

[0116] ,

[0117] in, This represents the ultimate shear stress of the joint. Let be the root area of ​​the shear key. The compressive strength of concrete (MPa) The area of ​​the pressure zone, The coefficient of friction, Let be the area of ​​frictional contact on the shear surface. This represents the average compressive stress in the concrete of the compression zone.

[0118] The root area of ​​the shear key determines its shear resistance. The compressive strength of concrete (MPa) is a basic mechanical property of concrete. The area of ​​the compression zone reflects the size of the pressure-bearing area in the joint. The area of ​​frictional contact on the shear surface is related to the area of ​​frictional force.

[0119] Furthermore, the formulas for calculating the ultimate shear stress of different types of joints are explained.

[0120] In practical applications, different formulas are required to calculate the ultimate shear stress for different types of joints. For planar section joints, the formula mentioned above, which considers shear keys and friction, is used. The calculation is performed using the same formula for joints with shear keys. ) calculation; however, for embedded steel plate shear key joints, due to differences in their structural characteristics and stress mechanisms, a more complex formula is required, which can be denoted as formula ( To calculate the ultimate shear stress.

[0121] When there is an embedded steel plate shear key in the joint and the reinforcement effect of the stirrups is considered, the formula for calculating the ultimate shear stress is further extended to:

[0122] ,

[0123] in, This represents the ultimate shear stress of the joint. Let be the root area of ​​the shear key. The compressive strength of concrete (MPa) The coefficient of friction, Let be the area of ​​frictional contact on the shear surface. This represents the average compressive stress in the concrete of the compression zone. The yield strength of the steel plate inside the shear key. The area of ​​the stirrups is... The area is the pressure zone.

[0124] By using the formulas for calculating the ultimate shear stress under different conditions, combined with the torsional plastic modulus of the joint section, the torsional bearing capacity of precast bridge pier joints can be accurately calculated, providing an important theoretical basis for the design, construction, and safety assessment of bridge piers. In practical engineering, appropriate formulas should be selected for calculation based on the specific type of joint and its stress conditions to ensure the accuracy and reliability of the calculation results.

[0125] S4. To accurately predict the peak bearing capacity and peak torque of precast assembled bridge piers under compression, bending, shear, and torsion loads, peak load calculations were performed on different precast assembled bridge piers based on the unified analysis equation for precast assembled bridge piers and the calculation formula for the torsional bearing capacity of joints. The results were then compared and analyzed with experimental results. Specific implementation steps and related content are as follows:

[0126] First, the interaction between prefabricated bridge piers under fixed axial force and compression-bending-shear-torsion loads is analyzed using the unified analysis equation for prefabricated bridge piers.

[0127] In this embodiment, the unified analysis equation for prefabricated bridge piers is used to analyze the interaction mechanism between the various parts of the prefabricated bridge pier under the conditions of fixed axial force and combined compression-bending-shear-torsion loads. This analysis is based on the unified analysis equation for prefabricated bridge piers. It enables a clear understanding of the mutual influence and constraints between load components under different load combinations.

[0128] Next, the torsional bearing capacity of the joints of the precast assembled bridge piers was calculated and analyzed using the joint torsional bearing capacity calculation formula, so as to obtain the analysis results of the torsional bearing capacity of the joints of the precast assembled bridge piers.

[0129] The embodiment is based on the calculation formula of the joint torsional bearing capacity. The calculation results can be further used to plot the interaction diagram of precast bridge piers under compression, bending, shear, and torsion loads under fixed axial force conditions. See [link to relevant documentation] for details. Figure 4 In the diagram, T represents torque, M represents bending moment, and V represents shear force. , and The peak torque, shear force, and bending moment of the precast segmental piers under pure torsion, pure shear, and pure bending loads are respectively provided, providing important reference information for the performance analysis of piers under different loads.

[0130] After completing the interaction analysis of the bridge piers and the calculation of the torsional bearing capacity of the joints, the results of the two are combined. By comprehensively considering the stress and bearing capacity of each part of the bridge pier, the peak load of different prefabricated bridge piers can be accurately obtained. This step requires a detailed analysis of the stress distribution and deformation of the bridge piers under different load combinations to ensure that the calculation results of the peak load can truly reflect the actual bearing capacity of the bridge piers.

[0131] To improve the accuracy and reliability of the method for determining the bearing capacity of precast bridge piers under compression, bending, shear, and torsion, test results of precast bridge piers were introduced and compared with the peak load obtained from the above implementation steps.

[0132] In an optional embodiment, the above-described method for determining the bearing capacity of prefabricated piers under compression, bending, shear, and torsion was used to calculate the peak loads of the five piers. The calculation results are shown in Table 1.

[0133] Table 1. Calculation Information for Peak Strength of Precast Segmental Piers under Compression, Bending, Shear, and Torsional Loads

[0134]

[0135] In Table 1, different bridge piers are named in the form of R-numbers, where the number part is used to represent the torsional ratio of the bridge pier. That is, the torsional ratios of bridge piers R-0, R-0.16 and R-1.4 are 0, 0.16 and 1.4, respectively.

[0136] As shown in Table 1, the method for determining the bearing capacity of precast bridge piers under compression, bending, shear, and torsion loads proposed in this invention can accurately predict the peak bearing capacity and torque of precast bridge piers under these loads. Further comparative analysis shows that the deviation between the calculated and experimental values ​​is controlled within 3.3%-5.8%, verifying the effectiveness of the calculation method.

[0137] Further analysis reveals that, except for pier R-1.4, the torsional bearing capacity provided by the pier body of the other precast piers is less than the torsional bearing capacity of the joints. Therefore, in pier R-1.4, the torsional bearing capacity is mainly provided by the joints, which also leads to a significant torsion phenomenon at the joint at the bottom of pier R-1.4. For the other four piers, their peak bearing capacity is lower than the shear bearing capacity of the joints, so the peak bearing capacity of these four piers is mainly provided by the pier body.

[0138] Finally, based on the comparative analysis results, the peak bearing capacity and peak torque of the precast assembled bridge piers under compression, bending, shear and torsion loads are accurately predicted.

[0139] Based on the above comparative analysis results, the peak bearing capacity and peak torque of precast assembled bridge piers under compression, bending, shear, and torsion loads can be accurately predicted. In this embodiment, the accuracy and reliability of the prediction results can be further improved by continuously optimizing the calculation method and parameter values, providing strong theoretical support and technical assurance for the design, construction, and safety assessment of precast assembled bridge piers. Furthermore, in practical engineering applications, the prediction results can be used to rationally design and optimize the pier structure, ensuring its safety and stability under complex loads.

[0140] Based on the analysis of the implementation content, it can be seen that the method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear and torsion has constructed a complete theoretical framework. From the stress failure model and analysis assumptions, to the derivation of the ultimate axial force expression, shear force balance equation, bending moment equation and torque equation, and then to the establishment of the unified analysis equation and the calculation formula for the torsional bearing capacity of joints, the relevant steps are closely linked to form a rigorous theoretical system, which provides a solid theoretical foundation for a deeper understanding of the mechanical behavior of precast assembled bridge piers under complex load conditions.

[0141] Meanwhile, by using the unified analysis equation for prefabricated bridge piers, the interaction between different parts of the bridge pier under fixed axial force and compression-bending-shear-torsion loads can be clearly revealed. The mutual influence and constraints between different load components (torque, shear force, axial force, bending moment) can be clarified, which helps to accurately understand the mechanical nature of bridge piers under complex stress states and provides a key reference direction for subsequent theoretical research and engineering practice.

[0142] Furthermore, the method sets reasonable analytical assumptions for the special stress conditions of precast and assembled bridge piers, including but not limited to concrete only bearing pressure, the stress characteristics of stirrups, the stress conditions of prestressed tendons, and the point of application of the resultant force in the compression zone. The above assumptions fully consider the actual material properties and stress characteristics of the bridge piers, making the theoretical analysis closer to the actual situation and improving the accuracy and reliability of the theoretical calculation results.

[0143] The above-mentioned method for determining the bearing capacity of precast bridge piers under bending, shear and torsion provides new theories and methods for the development of bridge engineering technology. It helps to solve the problem of evaluating the bearing performance of precast bridge piers under complex load conditions, improves the overall performance and safety of bridge piers, optimizes structural design, and further promotes innovation and development in bridge engineering technology in terms of structural design, construction technology and material application, thereby improving the overall technical level of bridge engineering.

[0144] Please see Figure 5 In an optional embodiment, the present invention also provides a system for determining the bearing capacity of precast assembled bridge piers under bending, shear, and torsion. This system includes a processor, an input device, an output device, and a memory, all interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to call the program instructions and execute the specific steps of the method and related embodiments for determining the bearing capacity of precast assembled bridge piers under bending, shear, and torsion provided by the present invention. The system for determining the bearing capacity of precast assembled bridge piers under bending, shear, and torsion of the present invention is structurally complete and objectively stable.

[0145] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for determining the bearing capacity of precast and assembled bridge piers under bending, shear, and torsion loads, characterized in that... Includes the following steps: Determine the stress failure model and analysis assumptions for precast bridge piers, and establish the ultimate axial force expression and shear force equilibrium equation for precast bridge piers based on the stress failure model and analysis assumptions. The bending moment equation and torque equation of prefabricated bridge piers are constructed, and the expression of the ultimate axial force, the shear force balance equation, the bending moment equation and the torque equation are derived to obtain the unified analysis equation of prefabricated bridge piers. Obtain the shear bearing capacity data and joint stress conditions of the precast and assembled bridge piers, and construct a calculation formula for the torsional bearing capacity of the joints based on the shear bearing capacity data and the joint stress conditions; Based on the unified analysis equation for prefabricated assembled bridge piers and the calculation formula for the torsional bearing capacity of joints, peak load calculations and experimental comparisons were conducted on different prefabricated assembled bridge piers to achieve prediction of the peak bearing capacity and peak torque of prefabricated assembled bridge piers under compression, bending, shear and torsion loads. The derivation of the ultimate axial force expression, the shear force equilibrium equation, the bending moment equation, and the torque equation to obtain the unified analysis equation for prefabricated assembled bridge piers includes: By substituting the ultimate axial force expression, the shear force balance equation and the torque equation into the bending moment equation, the unified analysis equation for prefabricated assembled bridge piers is derived. The unified analytical equation for the prefabricated assembled bridge piers satisfies the following relationship: ， in, To assess the torsional bearing capacity of precast and assembled bridge piers, This refers to the peak torque of precast segmental bridge piers under pure torsional load. To assess the shear bearing capacity of precast and assembled bridge piers, The shear force of precast segmental bridge piers under pure shear load. To test the ultimate compressive strength of precast and assembled bridge piers, The axial force of precast segmental bridge piers under pure compressive load. To improve the bending bearing capacity of precast and assembled bridge piers, The bending moment of a precast segmental bridge pier under pure bending load.

2. The method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The stress failure model and analytical assumptions for determining the precast assembled bridge piers include: The crack distribution and mechanical state of precast bridge piers were experimentally analyzed, and the experimental observation results of precast bridge piers were obtained. Based on the experimental observation results, a stress failure model for prefabricated assembled bridge piers was determined; Based on the stress-failure model and the experimental observation results, the analytical assumptions for precast assembled bridge piers are set. These assumptions include: concrete only bears compressive stress; stirrups intersecting the spiral crack only bear tensile stress and reach a yield state; unbonded prestressed tendons reach yield under compression-bending-shear and compression-bending-shear-torsion loads; the magnitude of prestress remains unchanged under compression-torsion loads; and the resultant force in the compression zone acts at the centroid of the compression zone. point.

3. The method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The establishment of the ultimate axial force expression and shear force equilibrium equation for prefabricated assembled bridge piers based on the stress failure model and the analytical assumptions includes: Based on the stress failure model and the analytical assumptions, the ultimate axial force expression and shear force equilibrium equation of the precast segmental assembled bridge pier under compression, bending, shear and torsion loads are derived. The expression for the limiting axial force satisfies the following relationship: ， in, To test the ultimate compressive strength of precast and assembled bridge piers, The resultant force provided to the concrete in the compression zone For the magnitude of the stress on the tension prestressing tendon, This refers to the force of a single prestressed tendon in the compression zone.

4. The method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion according to claim 3, characterized in that, The shear force equilibrium equation satisfies the following relationship: ， in, To assess the shear bearing capacity of precast and assembled bridge piers, For the stirrups to bear the force, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups.

5. The method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The bending moment equation and torque equation for constructing the prefabricated bridge piers include: Precast bridge piers around the centroid of the compression zone under compression, bending, shear and torsion loads The bending moment equation and torque equation at a point satisfy the following relationships: ， in, To improve the bending capacity of precast and assembled bridge piers, For the force of the prestressed tendons in the compression zone, For the prestressed tendons in the compression zone to Vertical distance between points For the magnitude of the stress on the tension prestressing tendon, For the prestressed tendons in the tension zone to Vertical distance between points For the tensile strength of concrete, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups; ， in, To assess the torsional bearing capacity of precast and assembled bridge piers, For the stirrups to bear the force, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The effective width of the cross section, The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height. This refers to the spacing between the stirrups.

6. The method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The acquisition of shear bearing capacity data and joint stress conditions of precast assembled bridge piers includes: A method for calculating the torsional bearing capacity of precast bridge pier joints under compression, bending, shear, and torsion loads is introduced. Based on the aforementioned torsional bearing capacity calculation method, the shear bearing capacity data of the prefabricated assembled bridge piers were obtained; A torsional bearing capacity analysis diagram of the joints of prefabricated bridge piers is drawn, and the stress condition of the joints of the prefabricated bridge piers is analyzed based on the torsional bearing capacity analysis diagram.

7. The method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The formula for calculating the torsional bearing capacity of a joint based on the shear bearing capacity data and the stress condition of the joint includes: The formula for calculating the torsional bearing capacity of the joint satisfies the following relationship: ， in, For the torsional bearing capacity of the joint, This represents the ultimate shear stress of the joint. The cross-sectional torsional plastic modulus of the joint.

8. The method for determining the bearing capacity of precast assembled bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The process of calculating and comparing peak loads on different precast assembled bridge piers based on the unified analysis equation for precast assembled bridge piers and the calculation formula for the torsional bearing capacity of joints, to predict the peak bearing capacity and peak torque of precast assembled bridge piers under compression, bending, shear, and torsional loads, includes: The interaction between prefabricated bridge piers under fixed axial force and compression-bending-shear-torsion loads is analyzed using the unified analysis equation of the prefabricated bridge piers. The analysis results of the joint torsional bearing capacity of precast assembled bridge piers were analyzed using the joint torsional bearing capacity calculation formula. The peak loads of different prefabricated piers were obtained by combining the interaction conditions and the analysis results of the joint torsional bearing capacity. The test results of prefabricated bridge piers were introduced; The test results and the peak load were compared and analyzed, and the comparison and analysis results were obtained. Based on the comparative analysis results, the peak bearing capacity and peak torque of prefabricated bridge piers under compression, bending, shear and torsion loads are predicted.

9. A system for determining the bearing capacity of precast and assembled bridge piers under bending, shear, and torsion conditions, characterized in that: The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to call the program instructions to execute the method for determining the bearing capacity of prefabricated bridge piers under bending, shear, and torsion as described in any one of claims 1-8.

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