Load-deformation determination method and system for precast bridge pier under compression-bending-shear-torsion action

Abstract

The present application relates to the technical field of bridge engineering, and provides a load-deformation determination method and system for a precast pier under compression-bending-shear-torsion action, which comprises determination of stage division and analysis assumption of a torsion moment-angle analysis model and a shear force-displacement analysis model of the precast pier under compression-bending-shear-torsion action; based on concrete mechanics parameters, a spatial truss model, the principle of virtual work and force balance, critical point calculation formulas of each stage of the two models are respectively established, and each model is simplified into a complete curve of the critical point connecting line; precast piers with different parameters are selected, the load-deformation analysis model is used to calculate the torsion moment-angle curve and the force-displacement curve, and comparison and verification are made with the test curve. The present application comprehensively considers the stiffness attenuation, crack development and deformation formation of each stress stage of the precast pier, can accurately reflect the dynamic relationship between the load and the deformation, and realizes accurate prediction of the change rule of the lateral force and the torsion moment of the precast pier with the loading displacement and the angle under compression-bending-shear-torsion load.

Description

Technical Field

[0001] This application relates to the field of bridge engineering technology, specifically to a method and system for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion. Background Technology

[0002] In the field of bridge engineering, precast bridge piers are widely used in the construction of highway and railway bridges due to their advantages such as convenient construction and short construction period. Especially in seismic fortification areas, they need to withstand the combined effects of compression, bending, shear and torsion caused by seismic loads. The load-deformation characteristics are the core basis for evaluating the structural safety and design rationality of bridge piers.

[0003] In existing technologies, the load-deformation analysis methods for precast bridge piers are mostly simplified from the theory of cast-in-place bridge piers. They do not fully consider the segmental nature and joint stress characteristics of precast assembled structures. Furthermore, when simulating the full stress process, they often ignore the stiffness decay law at different stages—for example, jumping directly to the limit state analysis after the elastic stage, and failing to quantify the stiffness reduction in the strengthening stage after the pier body cracks. This results in significant deviations between the theoretically calculated torsional stiffness and lateral stiffness and the actual stiffness of the bridge pier after cracking, and fails to accurately reflect the dynamic relationship between load and deformation. On the one hand, most methods do not combine the development of cracks in the pier body with the deformation, simplifying the calculation by only considering a single crack morphology, and ignoring the influence of crack angle changes on the stress of concrete inclined compression members and the transmission of tensile force in stirrups. On the other hand, when calculating the displacement or torsion angle at the top of the pier, only bending deformation is often considered, omitting key components such as rigid body rotation and shear deformation. Especially under combined loads of compression, bending, shear and torsion, the superposition effect of multiple deformation components is ignored, resulting in insufficient accuracy in predicting the variation of lateral force and torque of the pier with loading displacement and rotation angle. This makes it difficult to provide reliable theoretical support for the cross-sectional design and reinforcement optimization of precast piers, and easily leads to problems such as excessive reinforcement increasing costs or insufficient reinforcement causing safety hazards. Summary of the Invention

[0004] This application provides a method and system for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion. It comprehensively considers the stiffness attenuation, crack development, and deformation composition of the precast bridge pier at each stress stage, accurately reflecting the dynamic relationship between load and deformation. This enables precise prediction of the variation of lateral force and torque of precast bridge piers under compression, bending, shear, and torsion loads with loading displacement and rotation angle. This addresses the problem in existing technologies where the superposition effect of multiple deformation components is ignored under combined compression, bending, shear, and torsion loads, leading to insufficient accuracy in predicting the variation of lateral force and torque of bridge piers with loading displacement and rotation angle. This makes it difficult to provide reliable theoretical support for the cross-sectional design and reinforcement optimization of precast bridge piers, and easily results in problems such as excessive reinforcement increasing costs or insufficient reinforcement causing safety hazards.

[0005] The first aspect of this application provides a method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion, the method comprising:

[0006] The first model stage division and the first model analysis assumptions of the torque-rotation analysis model of precast bridge pier under compression, bending, shear and torsion are determined. Based on the stage division and analysis assumptions, the torque and rotation of the critical point a, the torque and rotation of the critical point b and the torque and rotation of the critical point c in the elastic stage are calculated respectively.

[0007] The second model stage division of the precast bridge pier shear force-displacement analysis model under compression-bending-shear-torsion action is determined. Based on the second model stage division and the second model analysis assumptions, the forces and displacements at critical points A, B, and C are calculated respectively.

[0008] Connect the critical points o, a, b, and c of the torque-rotation angle analysis model to form a complete torque-rotation angle curve. Connect the critical points O, A, B, and C of the shear force-displacement analysis model to form a complete force-displacement curve. Construct a precast bridge pier load-deformation analysis model based on the torque-rotation angle curve and the force-displacement curve.

[0009] Precast bridge piers with different parameters were selected, and their torque-rotation curves and force-displacement curves were calculated using the load-deformation analysis model. The theoretical curves were compared with the experimental curves to verify the accuracy of the model's prediction of the load-deformation law of precast bridge piers.

[0010] In one possible implementation, the first model analysis assumptions for determining the torque-rotation analysis model of precast bridge piers under compression-bending-shear-torsion loading include:

[0011] Construct a spatial truss model for the bridge piers;

[0012] In the spatial truss model of the bridge pier, the concrete is regarded as a diagonal compression member, the prestressed tendons are regarded as longitudinal reinforcement web members, and the stirrups are regarded as tension members.

[0013] In the spatial truss model of the bridge pier, the concrete diagonal compression members only bear compression, not shear or tension.

[0014] The lines of action of the resultant forces of the longitudinal reinforcement, stirrups, and diagonal compression members coincide;

[0015] The role of the pins in the prestressing tendons is ignored;

[0016] The torsional stiffness of the bridge pier is the series stiffness of each segment.

[0017] In one possible implementation, the step of calculating the torque and rotation angle at the elastic stage critical point a based on the stage division and analytical assumptions includes:

[0018] Calculate the torque at the critical point a in the elastic stage based on the tensile strength of concrete and the section modulus of section oa in the elastic stage;

[0019] Calculate the torsional stiffness of the precast pier at point a based on the shear modulus, moment of inertia of the section, and reduction factor.

[0020] Calculate the rotation angle of the elastic stage critical point a based on the torsional stiffness at point a and the torque at point a in the elastic stage.

[0021] In one possible implementation, the formula for calculating the torsional stiffness of point a is as follows:

[0022]

[0023] in, To determine the torsional stiffness of the precast bridge pier at point a, Shear modulus Let the moment of inertia of the cross section be... Let be the reduction factor for point a, which is 0.65.

[0024] In one possible implementation, the torque and rotation angle at critical point b are calculated based on the stage division and analytical assumptions, including:

[0025] The torque at critical point b is calculated based on the torsional plastic modulus and ultimate shear stress of the precast pier joint section.

[0026] Based on the stress generated by external forces in the reinforcement stage ab of the bridge pier spatial truss model, the torsional stiffness of the bridge pier in the reinforcement stage is calculated using the virtual work principle formula.

[0027] The rotation angle at critical point b is calculated based on the torsional stiffness during the strengthening stage and the torque at critical point b.

[0028] In one possible implementation, the formula for calculating the torsional stiffness of the strengthening stage is as follows:

[0029]

[0030] in, This refers to the torsional stiffness of a single segment of the bridge pier during the reinforcement stage. The sum of stresses generated by external forces, The stress generated by the unit torque, For the volume of the bridge pier, The elastic modulus of the bridge pier.

[0031] In one possible implementation, the formulas for calculating the force and displacement at the critical point A are as follows:

[0032]

[0033] Let I be the force at critical point A, and I be the moment of inertia of the cross section. The width of the bridge pier segment. Calculate the height of the bridge piers. This is the initial tension force of the prestressing tendons. To apply the load to the upper part of the bridge pier, The cross-sectional area of ​​the bridge pier;

[0034]

[0035] in, 'a' represents the displacement of the critical point A. Let E be the curvature of the bridge pier, and E be the elastic modulus of the bridge pier. Let be the force at critical point A, I be the moment of inertia of the cross section, and h be the calculated height of the pier.

[0036] In one possible implementation, the formulas for calculating the force and displacement at the critical point B are as follows:

[0037]

[0038] in, The force at critical point B, It is the vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the pressure zone; The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone; The spacing between the stirrups. For the tensile force of the stirrups, The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height.

[0039]

[0040] in, This represents the displacement of the critical point B. ρ is the elongation of the unbonded section of the prestressing tendon, D is the cross-sectional width, and c is the height of the compression zone. The force at critical point B, The stress distribution length of the prestressing tendon and yield strain The product of For bending stiffness, This refers to shear stiffness.

[0041] In one possible implementation, the process involves selecting precast bridge piers with different parameters, calculating their torque-rotation curves and force-displacement curves using the load-deformation analysis model, and comparing the theoretical curves with the experimental curves to verify the accuracy of the model's prediction of the load-deformation characteristics of the precast bridge piers. This includes:

[0042] The accuracy of the model is verified by comparing the positive load-deformation curve with the theoretically calculated curve.

[0043] This example provides a method for determining the load-deformation of precast bridge piers under compression-bending-shear-torsion loading. First, the stage division and analytical assumptions of the torque-rotation analysis model and the shear force-displacement analysis model for precast bridge piers under compression-bending-shear-torsion loading are determined. Based on concrete mechanical parameters, a space truss model, the principle of virtual work, and force balance, critical point calculation formulas for each stage of the two models are established, simplifying each model into a complete curve connecting the critical points. Precast bridge piers with different parameters are selected, and their torque-rotation curves and force-displacement curves are calculated using the load-deformation analysis model. These curves are then compared with experimental curves for verification. This technology can comprehensively consider the stiffness attenuation, crack development, and deformation of precast bridge piers at each stress stage, accurately reflect the dynamic relationship between load and deformation, and achieve precise prediction of the variation law of lateral force and torque of precast bridge piers with loading displacement and rotation under compression-bending-shear-torsion loads. In the existing technology, the superposition effect of multiple deformation components under combined compression-bending-shear-torsion loads is ignored, resulting in insufficient accuracy in predicting the variation law of lateral force and torque of bridge piers with loading displacement and rotation. This makes it difficult to provide reliable theoretical support for the cross-sectional design and reinforcement optimization of precast bridge piers, and easily leads to problems such as excessive reinforcement increasing costs or insufficient reinforcement causing safety hazards.

[0044] A second aspect of this application provides a load-deformation determination system for precast bridge piers under compression, bending, shear, and torsion, the system comprising:

[0045] The first determining unit is used to determine the first model stage division and the first model analysis assumptions of the torque-rotation angle analysis model of the precast bridge pier under compression, bending, shear and torsion. Based on the stage division and analysis assumptions, the torque and rotation angle at the critical point a, the torque and rotation angle at the critical point b and the torque and rotation angle at the critical point c of the elastic stage are calculated respectively.

[0046] The second determining unit is used to determine the second model stage division of the precast bridge pier shear force-displacement analysis model under compression-bending-shear-torsion action. Based on the second model stage division and the second model analysis assumptions, the force and displacement of critical point A, critical point B and critical point C are calculated respectively.

[0047] The processing unit is used to connect the critical points o, a, b, and c of the torque-rotation angle analysis model to form a complete torque-rotation angle curve, and to connect the critical points O, A, B, and C of the shear force-displacement analysis model to form a complete force-displacement curve. Based on the torque-rotation angle curve and the force-displacement curve, a precast bridge pier load-deformation analysis model is constructed.

[0048] The verification unit is used to select precast bridge piers with different parameters, calculate their torque-rotation curves and force-displacement curves using the load-deformation analysis model, and compare the theoretical curves with the experimental curves to verify the accuracy of the model's prediction of the load-deformation law of the precast bridge piers.

[0049] A third aspect of this application provides a terminal including a processor, an input device, an output device, and a memory, wherein the processor, input device, output device, and memory are interconnected, and the memory is used to store a computer program, the computer program including program instructions, and the processor is configured to call the program instructions to execute the steps of the method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion as described in the first aspect of this application.

[0050] A fourth aspect of this application provides a computer-readable storage medium storing a computer program for electronic data interchange, wherein the computer program causes a computer to perform some or all of the steps described in the method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion in the first aspect of this application.

[0051] A fifth aspect of this application provides a computer program product, wherein the computer program product includes a non-transitory computer-readable storage medium storing a computer program operable to cause a computer to perform some or all of the steps described in the load-deformation determination method for precast bridge piers under compression, bending, shear, and torsion in the first aspect of this application. The computer program product may be a software installation package. Attached Figure Description

[0052] 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.

[0053] Figure 1 This application provides a schematic diagram of the overall process for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion.

[0054] Figure 2 This application provides a schematic diagram of the torque-rotation curve of a precast segmental column under compression, bending, shear and torsion.

[0055] Figure 3 This application provides a schematic diagram of a variable-angle spatial truss model for a precast segmental column under compression, bending, shear, and torsion.

[0056] Figure 4 This application provides a schematic diagram of the torsional bearing capacity of the joint of a precast segmental column under compression, bending, shear and torsion.

[0057] Figure 5 This application provides a schematic diagram of the cross-sectional shear flow distribution of a variable-angle spatial truss model of a precast segmental column under compression, bending, shear, and torsion.

[0058] Figure 6 This application provides a schematic diagram of the stress distribution on the left side of a variable-angle space truss model of a precast segmental column under compression, bending, shear, and torsion.

[0059] Figure 7 This application provides a schematic diagram showing the angle between the torsional stiffness of a precast segmental column pier and the horizontal direction of the crack under compression, bending, shear and torsion.

[0060] Figure 8 This application provides a schematic diagram of the shear force-displacement curve of a precast segmental column under compression, bending, shear, and torsion.

[0061] Figure 9 This application provides a schematic diagram comparing the experimental and theoretical force-displacement curves of a precast segmental column under compression, bending, shear, and torsion.

[0062] Figure 10 This application provides a schematic diagram comparing the experimental and theoretical torque-rotation curves of a precast segmental column under compression, bending, shear, and torsion.

[0063] Figure 11 This application provides a schematic diagram of the overall structure of a load-deformation determination system for precast bridge piers under compression, bending, shear, and torsion.

[0064] Figure 12 This application provides a schematic diagram of the structure of a terminal.

[0065] Figure label:

[0066] First determining unit-1, second determining unit-2, processing unit-3, verification unit-4. Detailed Implementation

[0067] 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, and 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.

[0068] The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0069] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0070] The load-deformation determination method for precast bridge piers under compression, bending, shear, and torsion is applied to the load-deformation determination system for precast bridge piers under compression, bending, shear, and torsion. Figure 1 A schematic diagram illustrating the overall flow of a method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion is shown. Figure 1 As shown, it includes:

[0071] S1. Determine the first model stage division and the first model analysis assumptions of the torque-rotation analysis model of the precast bridge pier under compression, bending, shear and torsion. Calculate the torque and rotation angle at the critical point a, critical point b and critical point c of the elastic stage according to the stage division and analysis assumptions.

[0072] Among them, under the action of compression, bending, shear and torsion loads, the torque-rotation curve of precast assembled bridge piers can be divided into three stages: the elastic stage oa, the strengthening stage ab, and the degradation stage bc, as shown in the figure. Figure 2 As shown, where, Figure 2 The parameters include: Let a be the torsional stiffness at point a; The angle at point a; Let b be the torsional stiffness. The angle at point b; Let c be the torsional stiffness. The angle at point c; This represents the torsional stiffness in the elastic stage (oa). In the elastic stage (oa), no cracks appear in the precast pier body, and the pier deformation is elastic. In the strengthening stage (ab), cracks begin to appear in the pier body. When the torsional strength of the pier body exceeds the torsional strength of the joint, the pier joint will rotate. In the degradation stage (bc), the pier concrete begins to spall, and the torque decreases as the degree of spalling increases.

[0073] In the elastic stage (oa), the torque-rotation curve of the precast pier in the elastic stage (oa) is obtained by solving for the torque and rotation at the critical point (a). At the critical point (a), cracks begin to appear in the pier body of the precast pier, and at this time, the joints of the pier have not yet opened. The stress behavior of the precast pier is the same as that of the cast-in-place pier. Therefore, the torsional lateral force of the pier body will definitely be lower than the torsional force of the joint. In the elastic stage, the influence of bending moment and shear force on the magnitude of torque can be ignored.

[0074] The calculation of the torque and rotation angle at the critical point a of the elastic stage, based on the stage division and analytical assumptions, includes:

[0075] Based on the tensile strength of concrete and the section modulus of section oa in the elastic stage, the torque at the critical point a in the elastic stage is calculated. The formula for calculating the torque at the critical point a is shown in Figure 1-1.

[0076] Calculate the torsional stiffness of the precast pier at point a based on the shear modulus, moment of inertia of the section, and reduction factor.

[0077] Calculate the rotation angle of the elastic stage critical point a based on the torsional stiffness at point a and the torque at point a in the elastic stage.

[0078] Specifically, the formula for calculating the torque at critical point a is shown in 1-1, the formula for calculating the torsional stiffness at point a is shown in 1-2, and the rotation angle at critical point a in the elastic stage is shown in 1-3. Formula 1-3 is derived from formulas 1-1 to 1-2, as shown below:

[0079] (1-1)

[0080] in, Let a be the torsional stiffness at point a. It refers to the tensile strength of concrete; Let $oa$ be the section modulus of the elastic stage.

[0081] (1-2)

[0082] in, The torsional stiffness of the precast bridge pier at point a; I is the shear modulus; I is the moment of inertia of the cross section; Let be the reduction factor for point a, which is 0.65.

[0083] (1-3)

[0084] in, The angle at point a; The torsional stiffness of the precast bridge pier at point a; Let be the torsional stiffness at point a.

[0085] In the reinforcement stage (ab), due to the appearance of cracks in the pier body, the torsional stiffness of the precast pier in the reinforcement stage is smaller than that in the elastic stage. The torsional stiffness in this stage can be simplified by analyzing the cracked pier using a spatial truss model. A single-segment spatial truss model is shown below. Figure 3 As shown, where F is the horizontal force, T is the torque, M is the bending moment, V is the shear force, and s is the stirrup spacing. Let the angle between the concrete crack on the right and the direction of the pier height be denoted as . For ease of calculation, the following assumptions are made for the first model analysis:

[0086] (1) In the variable angle space truss model, concrete is regarded as a diagonal compression member, prestressed tendons are regarded as longitudinal reinforcement web members, and stirrups are regarded as tension members.

[0087] (2) The angles between the concrete cracks on the top, bottom, left, and right sides and the height of the pier are respectively , , and ( Figure 3 This shows the angle between the concrete crack on the right side of a variable-angle space truss model and the pier height direction. The other three sides are similar (not shown in the diagram).

[0088] (3) Concrete diagonal compression members only bear compressive force, not shear force or tension force.

[0089] (4) The lines of action of the longitudinal reinforcement, stirrups and diagonal compression members coincide.

[0090] (5) The pin effect of prestressing tendons is ignored.

[0091] (6) The torsional stiffness of the pier is the series stiffness of each segment.

[0092] In one possible implementation, the step of calculating the torque and rotation angle at critical point b based on the stage division and analysis assumptions includes:

[0093] The torque at critical point b is calculated based on the torsional plastic modulus and ultimate shear stress of the precast pier joint section.

[0094] Based on the stress generated by external forces in the reinforcement stage ab of the bridge pier spatial truss model, the torsional stiffness of the bridge pier in the reinforcement stage is calculated using the virtual work principle formula.

[0095] The rotation angle at critical point b is calculated based on the torsional stiffness during the strengthening stage and the torque at critical point b.

[0096] 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 drawn in this embodiment, as shown below. Figure 4 As shown, where Figure 4 The parameters include: V for shear force, T for torque, and N for 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 4 This helps to visually present the variation of the load-bearing capacity of joints under different stress combinations, such as Figure 2 As shown, the torque-rotation curve of the precast assembled bridge pier during the reinforcement stage (ab) is obtained by connecting the torque and rotation angle at critical points a and b. At the critical point b, the torque of the bridge pier is the peak torque. The magnitude of the torque at point b can be calculated using formulas 1-4. The formula for calculating the torque at the critical point b is as follows:

[0097] (1-4)

[0098] in, This represents the ultimate shear stress of the joint. The cross-sectional torsional plastic modulus of the joint.

[0099] Furthermore, based on the principle of virtual work, the formula can be obtained:

[0100] (1-5)

[0101] in, Stress generated by external forces; The stress corresponding to a value of 1; dv is the volume of the rod along length dz; This refers to the torsional stiffness of a single segment of the bridge pier during the reinforcement stage. For the integral variables of the coordinate parameters along the length of the corresponding pier member, when... When the value is 1, Formula 1-5 can be changed to Formula 1-6 to calculate the torsional stiffness of the bridge pier in the strengthening stage.

[0102] (1-6)

[0103] in, This refers to the torsional stiffness of a single segment of the bridge pier during the reinforcement stage. The sum of stresses generated by external forces, The stress generated by the unit torque, For the volume of the bridge pier, The elastic modulus of the bridge pier.

[0104] Furthermore, the shear flow distribution on each face of the space truss model is as follows: Figure 5 As shown, where, Figure 5 The parameters include: Shear flow generated by torque , Shear flow generated by shear force V represents shear force, T represents torque, u represents top, l represents left, r represents right, and b represents bottom. Let be the effective height of the pier segment, h be the height of the pier segment, and t be the wall thickness of the pier interface. Effective width of the pier segment; shear flow generated by torque. Shear flow generated by shear force distributed on four sides Distributed only on two sides, calculated according to formulas 1-7 and 1-8 respectively, as shown below:

[0105] (1-7)

[0106] in, Shear flow generated by torque, The torque at critical point b. The effective width of the cross section, The effective height of the cross section.

[0107] (1-8)

[0108] in, Shear flow generated by shear force. Let b be the shear force at the critical point. The effective height of the cross section.

[0109] Furthermore, based on the principle of force balance, the stress of each member on each surface is calculated, including the stress of the concrete diagonal compression member on the four surfaces (top, bottom, left, and right). , , and Calculate according to formulas 1-9, 1-10, 1-11, and 1-12 respectively, as shown below:

[0110] (1-9)

[0111] (1-10)

[0112] (1-11)

[0113] (1-12)

[0114] Where t is the wall thickness of the pier interface; Shear flow generated by torque; Shear flow generated by shear force; The torque at the critical point b; The angle between the concrete crack on the bridge pier and the direction of the pier height; The angle between the concrete crack beneath the pier and the pier height direction; The angle between the concrete crack on the left side of the pier and the direction of the pier height; The angle between the concrete crack on the right side of the pier and the pier height direction; Let b be the shear force at the critical point.

[0115] The stress distribution on the left side section of the pier segment is as follows: Figure 6 As shown, where, Figure 6 The parameters in the text include: Shear flow generated by torque; Shear flow generated by shear force; The area of ​​the longitudinal reinforcement web members; The stress on the left side of the stirrup tie rod; The stress in the longitudinal reinforcement web members on the left side is given; according to the vertical force balance, the stress in the stirrup tie members on the left side can be obtained. Formula 1-13. Similarly, the stress of the stirrups on the upper, lower, and right sides... , and The distribution can be calculated using formulas 1-13, 1-14, and 1-15, as shown below:

[0116] (1-13)

[0117] (1-14)

[0118] (1-15)

[0119] (1-16)

[0120] In the formula, The effective area of ​​the cross section, for and The product; s is the area of ​​the stirrups; s is the spacing between the stirrups; The torque at the critical point b; The shear force at the critical point b; The angle between the concrete crack on the bridge pier and the direction of the pier height; The angle between the concrete crack beneath the pier and the pier height direction; The angle between the concrete crack on the left side of the pier and the direction of the pier height; The angle between the concrete crack on the right side of the pier and the direction of the pier height.

[0121] Furthermore, based on the moment balance of each section of the pier segment, the stresses of the upper left, upper right, lower left, and lower right longitudinal reinforcement web members can be calculated using formulas 1-17, 1-18, 1-19, and 1-20. , , and As shown below:

[0122] (1-17)

[0123] (1-18)

[0124] (1-19)

[0125] (1-20)

[0126] In the formula, t is the wall thickness of the pier interface; The angle between the concrete crack on the bridge pier and the direction of the pier height; The angle between the concrete crack beneath the pier and the pier height direction; The angle between the concrete crack on the left side of the pier and the direction of the pier height; The angle between the concrete crack on the right side of the pier and the pier height direction; The torque at the critical point b; The shear force at the critical point b; Let be the bending moment at the critical point b; The effective height of the cross-section; This represents the area of ​​the prestressed tendon web members. ' is the area of ​​the prestressed tendons in the compression zone.

[0127] Furthermore, when When the stress is 1, the stresses in the concrete diagonal compression members and stirrup tie members on each surface can be calculated using formulas 1-21 and 1-22, respectively. The stresses in the upper left, upper right, lower left, and lower right longitudinal reinforcement web members can be calculated using formulas 1-23, 1-24, 1-25, and 1-26, respectively, as shown in the following formulas:

[0128] (i=u,b,l,r) (1-21)

[0129] (i=u,b,l,r) (1-22)

[0130] (1-23)

[0131] (1-24)

[0132] (1-25)

[0133] (1-26)

[0134] In the formula, The effective area of ​​the cross section is and The product; This represents the area of ​​the stirrups; The area of ​​the longitudinal reinforcement web members; The angle between the concrete crack on the bridge pier and the direction of the pier height; The angle between the concrete crack beneath the pier and the pier height direction; The angle between the concrete crack on the left side of the pier and the direction of the pier height; The angle between the concrete crack on the right side of the pier and the pier height direction; The effective height of the cross section,

[0135] Furthermore, based on the above formulas, the strain energy of concrete diagonal compression members, stirrup tie members, and longitudinal reinforcement web members can be calculated according to formulas 1-27, 1-28, and 1-29.

[0136] (1-27)

[0137] (1-28)

[0138] (1-29)

[0139] In the formula, t is the wall thickness of the pier interface; The elastic modulus of concrete; The elastic modulus of the stirrup; The effective area of ​​the cross section is and The product; The angle between the concrete crack on the bridge pier and the direction of the pier height; The angle between the concrete crack beneath the pier and the pier height direction; The angle between the concrete crack on the left side of the pier and the direction of the pier height; The angle between the concrete crack on the right side of the pier and the pier height direction; Let be the bending moment at the critical point b; The torque at the critical point b; The shear force at the critical point b; This represents the area of ​​the longitudinal reinforcement web members.

[0140] Substituting equations 1-27 to 1-29 into equation 1-6 yields the reciprocal of the torsional stiffness of the bridge pier segment, as shown in equation 1-30:

[0141] (1-30)

[0142] In the formula, The effective area of ​​the cross section is and The product; This represents the area of ​​the stirrups; This represents the cross-sectional area of ​​the upper longitudinal reinforcement web member; This represents the cross-sectional area of ​​the lower longitudinal reinforcement web members; Effective diameter of the pier cross section; The depth of the core concrete; This is the initial elastic modulus; The elastic modulus of the stirrup; The elastic modulus of the longitudinal reinforcement; The angle between the concrete crack on the bridge pier and the direction of the pier height; The angle between the concrete crack beneath the pier and the pier height direction; The angle between the concrete crack on the left side of the pier and the direction of the pier height; The angle between the concrete crack on the right side of the pier and the pier height direction; This is the ratio of the elastic modulus of concrete to that of longitudinal reinforcement. The width of the core concrete; The height of the core concrete.

[0143] As shown in formulas 1-27 to 1-29, the torsional stiffness of the bridge pier is closely related to the angle of the crack. A schematic diagram of the angle between the crack and the horizontal direction is shown below. Figure 7 As shown, where, Figure 7 The meanings of each parameter include: The height of a certain face of the bridge pier; The angle between a concrete crack on a certain surface of the bridge pier and the direction of the pier height. The resultant force of the concrete diagonal compression member; This refers to the yield stress of the prestressed tendon. N is the area of ​​the prestressing tendon; N is the axial force. This represents the yield stress of the stirrups. This represents the area of ​​the stirrups; Let the shear flow be the shear flow on a certain face of the bridge pier. According to the vertical force balance, we can obtain equation 1-31, and from equation 1-32, we can see that the crack inclination angle is related to the shear flow on each face and the force of the stirrups.

[0144] (1-31)

[0145] In the formula, The angle between a concrete crack on a certain surface of the bridge pier and the direction of the pier height. This represents the area of ​​the stirrups; s is the stirrup yield stress; s is the stirrup spacing; This refers to the shear flow on a certain face of the bridge pier.

[0146] When the stirrups on all four sides (top, bottom, left, and right) yield, the cotangent of the concrete crack inclination angle is positively correlated with the shear flow. The side with the larger shear flow is the left side in this paper, and the crack inclination angle is... The larger the cotangent, the greater it can be calculated using formula 1-31. Similarly, the surface with smaller shear flow is the right-hand surface in this paper, and the crack inclination angle of this surface is... The cotangent is also the smallest, which can be calculated according to formula 1-32. Since the shear flow magnitudes on the upper and lower surfaces are equal, the cotangent magnitudes of the crack inclination angles on these two surfaces are also equal.

[0147] (1-32)

[0148] (1-33)

[0149] In the formula, The angle between the concrete crack on the bridge pier and the direction of the pier height; The angle between the concrete crack beneath the pier and the pier height direction; The angle between the concrete crack on the left side of the pier and the direction of the pier height; The angle between the concrete crack on the right side of the pier and the pier height direction; The torque at the critical point b; The shear force at the critical point b; This represents the effective width of the cross-section.

[0150] Among them, according to Figure 7 Analysis of the isolated body reveals that the vertical force equilibrium equation 1-34 represents the balance between the stirrup force and the vertical component of the concrete inclined compression member. The horizontal force equilibrium equation 1-35 represents the balance between the resultant force of the prestressing tendon tension and the horizontal component and axial force of the concrete inclined compression member. Combining equations 1-34 and 1-35 eliminates the resultant force of the concrete inclined compression member. Equation 1-36 can be obtained.

[0151] (1-34)

[0152] (1-35)

[0153] (1-36)

[0154] In the formula, The angle between a concrete crack on a certain surface of the bridge pier and the direction of the pier height. This represents the area of ​​the stirrups; This represents the yield stress of the stirrups. The yield stress of the longitudinal reinforcement; s represents the height of a certain face of the bridge pier; s represents the stirrup spacing; N represents the axial force; The area of ​​the prestressing tendons; This represents the yield stress of the prestressed tendon.

[0155] Based on formulas 1-30 to 1-36, the torsional stiffness of a single pier segment during the strengthening stage can be obtained. The torsional stiffness of the pier during strengthening should be [amount missing] times the torsional stiffness of a single segment. During the reinforcement stage, the rotation angle of the bridge pier can be calculated according to formula 1-37.

[0156] (1-37)

[0157] In the formula, The torque at the critical point b; Let b be the torsional stiffness at the critical point.

[0158] In the degradation stage bc, the torque-rotation curve of the precast pier in this stage is obtained by connecting the torque and rotation angle at points b and c. At point c, the pier's torque is the ultimate torque, which is 0.85 times the torque value, yielding formula 1-38. Based on the stiffness change data obtained from experiments, it is found that the torsional stiffness in the degradation stage is approximately half that in the strengthening stage. Therefore, the rotation angle at point c is given by formula 1-39, as shown below:

[0159] (1-38)

[0160] (1-39)

[0161] In the formula, The torque at the critical point b; Let be the torsional stiffness at the critical point b.

[0162] S2. Determine the second model stage division of the precast bridge pier shear force-displacement analysis model under compression, bending, shear and torsion. Calculate the force and displacement at critical point A, critical point B and critical point C respectively based on the second model stage division and the assumptions of the second model analysis.

[0163] Among them, under the action of compression, bending, shear and torsion loads, the force-displacement curve of precast assembled bridge piers can be divided into three stages: the decompression stage OA, the yielding stage AB, and the degradation stage BC, as shown in the figure. Figure 8 As shown, where, Figure 8 The meanings of each parameter include: The force at critical point A; The force at the critical point B; The force at the critical point C; This represents the displacement of the critical point A. This represents the displacement of the critical point B. This represents the displacement of the critical point C. The shear force-displacement curve represents the lateral stiffness during the decompression stage OA. During OA, no openings appear at the precast pier joints, but at the critical point A, the joints at the pier bottom are about to open, and the height of the compression zone begins to be less than the cross-sectional width. During the yielding stage AB, the unbonded prestressing tendons at the pier bottom begin to deform, and the prestress increases. At the critical point B, the stress in the unbonded prestressing tendons reaches the yield stress, and the bearing capacity reaches its maximum value. During the degradation stage BC, the concrete at the pier bottom begins to spall, and the bearing capacity decreases with increasing spalling. To avoid complex calculations, the force-displacement curve of the precast pier under compression, bending, shear, and torsion loads is simplified to the line connecting O, A, B, and C.

[0164] Furthermore, the force-displacement curve of the precast assembled bridge pier during the decompression stage OA is obtained by solving for the force and displacement at point A. At the critical point A, the height of the compression zone of the pier is equal to the cross-sectional height, and the force equilibrium equation is satisfied. In addition, this stage is essentially in the elastic stage, and the influence of torque on shear force during this stage can be neglected. Therefore, the force at the critical point A... and displacement The solution can be obtained using the following formulas 2-1 to 2-2:

[0165] (2-1)

[0166] in, Let I be the force at critical point A, and I be the moment of inertia of the cross section. The width of the bridge pier segment. Calculate the height of the bridge piers. This is the initial tension force of the prestressing tendons. To apply the load to the upper part of the bridge pier, The cross-sectional area of ​​the bridge pier;

[0167] (2-2)

[0168] in, 'a' represents the displacement of the critical point A. Let E be the curvature of the bridge pier, and E be the elastic modulus of the bridge pier. Let I be the force at critical point A, I be the moment of inertia of the cross section, and h be the calculated height of the pier.

[0169] Furthermore, the force-displacement curves of the precast assembled bridge pier during the reinforcement stage AB are obtained by connecting the force and displacement at critical points A and B. At the critical point B, the force on the bridge pier is the peak force, and its magnitude... It can be calculated using the unified strength theory, and the calculation formula is shown in Figure 2-3:

[0170] (2-3)

[0171] in, The force at critical point B, The vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the compression zone; The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the pressure zone; The spacing between the stirrups. For the tensile force of the stirrups, The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height.

[0172] Among them, the horizontal displacement of the pier top It mainly consists of rigid body rotation, shear deformation, and bending deformation, which can be expressed as Equation 2-4, as shown below:

[0173] (2-4)

[0174] in, This represents the displacement of the critical point B. denoted as , where D is the elongation of the unbonded section of the prestressing tendon, and c is the cross-sectional width and the height of the compression zone. The force at critical point B, The stress distribution length of the prestressing tendon and yield strain The product of For bending stiffness, This refers to shear stiffness.

[0175] Furthermore, the force-displacement curve of the precast assembled bridge pier during the degradation stage BC is obtained by connecting the force and displacement at critical points B and C. At critical point C, the force on the pier is the ultimate bearing capacity, which is 0.85 times its magnitude. At this point, the horizontal displacement at the top of the pier mainly consists of rigid body rotation, shear deformation, and bending deformation, and can still be calculated according to 2-4.

[0176] S3. Connect the critical points o, a, b, and c of the torque-rotation angle analysis model to form a complete torque-rotation angle curve. Connect the critical points O, A, B, and C of the shear force-displacement analysis model to form a complete force-displacement curve. Construct a precast bridge pier load-deformation analysis model based on the torque-rotation angle curve and the force-displacement curve.

[0177] S4. Select precast bridge piers with different parameters, and use the load-deformation analysis model to calculate their torque-rotation curves and force-displacement curves. Compare the theoretical curves with the experimental curves to verify the accuracy of the model's prediction of the load-deformation law of the precast bridge piers.

[0178] Based on the proposed unified strength theory calculation model and load-deformation curve calculation method for prefabricated assembled bridge piers under compression, bending, shear, and torsion, the torque-rotation curves and force-displacement curves for piers R-0, R-0.16, R-1.4, R-1.4k, and R-∞ were calculated. Since pier R-0 is not subjected to torque, and due to significant displacement of some piers during the experiment, the curves exhibited asymmetry. Therefore, this example verification section only compares the positive load-deformation curves with the theoretically calculated curves. A schematic diagram comparing the experimental and theoretical force-displacement curves for piers R-0, R-0.16, R-1.4, and R-1.4k is shown below. Figure 9 As shown, Figure 9 middle, Figure 9 In the figure, 'a' represents the experimental and theoretical force-displacement curves of pier R-0; Figure 9 In the figure, b represents the experimental and theoretical force-displacement curves for pier R-0.16. Figure 9 In the figure, 'c' represents the experimental and theoretical force-displacement curves of pier R-1.4. Figure 9d represents the experimental and theoretical force-displacement curves for pier R-1.4k. Comparison of the theoretical and experimental force-displacement curves reveals that the proposed calculation method can accurately predict the variation of the force-displacement curves. In the elastic stage, the theoretically calculated force-displacement curves largely coincide with the experimental curves. In the strengthening stage, the theoretically calculated lateral forces of piers R-0 and R-0.16 are higher than the experimental values, while the theoretically calculated lateral forces of piers R-1.4 and R-1.4k are lower than the experimental values. This is because piers R-0 and R-0.16 have smaller torsional ratios, meaning they are primarily subjected to bending, and the torque has a relatively small impact on their bending stiffness. However, piers R-1.4 and R-1.4k have larger torsional ratios, meaning they are primarily subjected to torsion, and the torque reduces their bending stiffness. Due to limited experimental data, this paper did not consider the influence of torque on bending stiffness and calculated the lateral forces based on the bending stiffness under compression-bending conditions, resulting in lower lateral forces than the experimental values. During the degradation stage, the calculated force-displacement curve of the pier showed a similar downward trend to that of the experiment. A comparison of the initial flexural stiffness obtained from the experiment and the calculation revealed that the calculated value was larger than the experimental value, with a deviation range of 9.4%-15.8%. The reason for the larger calculated initial flexural stiffness is that the calculation assumes the concrete of the pier to be completely homogeneous, while this ideal state does not exist in reality, resulting in lower concrete stiffness than the ideal state.

[0179] The experimental and theoretical torque-rotation curves for bridge piers R-∞, R-0.16, R-1.4, and R-1.4k are shown in the schematic diagram below. Figure 10 As shown, Figure 10 In the figure, 'a' represents the experimental and theoretical torque-rotation curves for the bridge pier at radius R-∞. Figure 10 In the figure, b represents the experimental and theoretical torque-rotation curves for pier R-0.16. Figure 10 In the figure, 'c' represents the experimental and theoretical torque-rotation curves for pier R-1.4. Figure 10 In the figure, d represents the experimental and theoretical torque-rotation angle curves for pier R-1.4k. Comparing the theoretical and experimental torque-rotation angle curves reveals that the proposed calculation method can accurately predict the variation of torque with pier rotation angle. In the elastic stage, the calculated torque-rotation angle curve of the pier basically coincides with the experimental curve. In the strengthening stage, due to theoretical simplification, there is an acceptable deviation between the calculated torque-rotation angle curve and the experimental curve. In the degradation stage, the trend of the theoretically calculated torque decreasing with the torsional angle is basically consistent with the experimental results. Table 4-1 summarizes the calculated and experimental values ​​of the initial torsional stiffness and cracked torsional stiffness of the precast pier. The deviation range of the calculated and experimental values ​​of the initial torsional stiffness is 6.1%-9.7%, and the deviation range of the calculated and experimental values ​​of the cracked torsional stiffness is 0.8%-8.2%.

[0180] Table 4-1 is shown below:

[0181]

[0182] In summary, the load-deformation calculation model of the precast bridge pier under compression, bending, shear and torsion loads proposed in this example has good consistency with the test results and can be used to predict the variation of lateral force and torque of precast bridge pier under compression, bending, shear and torsion loads with loading displacement and bridge pier rotation angle.

[0183] This example provides a method for determining the load-deformation of precast bridge piers under compression-bending-shear-torsion loading. First, the stage division and analytical assumptions of the torque-rotation analysis model and the shear force-displacement analysis model for precast bridge piers under compression-bending-shear-torsion loading are determined. Based on concrete mechanical parameters, a space truss model, the principle of virtual work, and force balance, critical point calculation formulas for each stage of the two models are established, simplifying each model into a complete curve connecting the critical points. Precast bridge piers with different parameters are selected, and their torque-rotation curves and force-displacement curves are calculated using the load-deformation analysis model. These curves are then compared with experimental curves for verification. This technology can comprehensively consider the stiffness attenuation, crack development, and deformation of precast bridge piers at each stress stage, accurately reflect the dynamic relationship between load and deformation, and achieve precise prediction of the variation law of lateral force and torque of precast bridge piers with loading displacement and rotation under compression-bending-shear-torsion loads. In the existing technology, the superposition effect of multiple deformation components under combined compression-bending-shear-torsion loads is ignored, resulting in insufficient accuracy in predicting the variation law of lateral force and torque of bridge piers with loading displacement and rotation. This makes it difficult to provide reliable theoretical support for the cross-sectional design and reinforcement optimization of precast bridge piers, and easily leads to problems such as excessive reinforcement increasing costs or insufficient reinforcement causing safety hazards.

[0184] For those consistent with the above, please refer to Figure 11 , Figure 11 This application provides a structural schematic diagram of a load-deformation determination system for precast bridge piers under compression, bending, shear, and torsion. (See attached diagram.) Figure 11 As shown, the system includes:

[0185] The first determining unit 1 is used to determine the first model stage division and the first model analysis assumptions of the precast bridge pier torque-rotation angle analysis model under compression, bending, shear and torsion. Based on the stage division and analysis assumptions, the torque and rotation angle of the elastic stage critical point a, the torque and rotation angle of the critical point b and the torque and rotation angle of the critical point c are calculated respectively.

[0186] The second determining unit 2 is used to determine the second model stage division of the precast bridge pier shear force-displacement analysis model under compression-bending-shear-torsion action. Based on the second model stage division and the second model analysis assumptions, the force and displacement of critical point A, critical point B and critical point C are calculated respectively.

[0187] Processing unit 3 is used to connect the critical points o, a, b, and c of the torque-rotation angle analysis model to form a complete torque-rotation angle curve, and to connect the critical points O, A, B, and C of the shear force-displacement analysis model to form a complete force-displacement curve. Based on the torque-rotation angle curve and the force-displacement curve, a precast bridge pier load-deformation analysis model is constructed.

[0188] Verification unit 4 is used to select precast bridge piers with different parameters, calculate their torque-rotation curves and force-displacement curves using the load-deformation analysis model, compare the theoretical curves with the experimental curves, and verify the accuracy of the model's prediction of the load-deformation law of precast bridge piers.

[0189] For examples consistent with the above embodiments, please refer to... Figure 12 , Figure 12 A schematic diagram of a terminal structure provided in an embodiment of this application is shown in the figure. It includes a processor, an input device, an output device, and a memory. The processor, input device, output device, and memory are interconnected. The memory is used to store a computer program, which includes program instructions. The processor is configured to call the program instructions. The program includes instructions for performing the following steps.

[0190] The first model stage division and the first model analysis assumptions of the torque-rotation analysis model of precast bridge pier under compression, bending, shear and torsion are determined. Based on the stage division and analysis assumptions, the torque and rotation of the critical point a, the torque and rotation of the critical point b and the torque and rotation of the critical point c in the elastic stage are calculated respectively.

[0191] The second model stage division of the precast bridge pier shear force-displacement analysis model under compression-bending-shear-torsion action is determined. Based on the second model stage division and the second model analysis assumptions, the forces and displacements at critical points A, B, and C are calculated respectively.

[0192] Connect the critical points o, a, b, and c of the torque-rotation angle analysis model to form a complete torque-rotation angle curve. Connect the critical points O, A, B, and C of the shear force-displacement analysis model to form a complete force-displacement curve. Construct a precast bridge pier load-deformation analysis model based on the torque-rotation angle curve and the force-displacement curve.

[0193] Precast bridge piers with different parameters were selected, and their torque-rotation curves and force-displacement curves were calculated using the load-deformation analysis model. The theoretical curves were compared with the experimental curves to verify the accuracy of the model's prediction of the load-deformation law of precast bridge piers.

[0194] In this example, the stage division and analysis assumptions of the torque-rotation analysis model and shear-displacement analysis model for precast bridge piers under compression-bending-shear-torsion loading are first determined. Based on concrete mechanical parameters, spatial truss model, virtual work principle, and force balance, the critical point calculation formulas for each stage of the two models are established, simplifying each model into a complete curve connecting the critical points. Precast bridge piers with different parameters are selected, and their torque-rotation curves and force-displacement curves are calculated using the load-deformation analysis model. The results are then compared with experimental curves to verify that this example can comprehensively consider the various loads on precast bridge piers. The stiffness attenuation, crack development, and deformation during the stress stage can accurately reflect the dynamic relationship between load and deformation, enabling precise prediction of the variation of lateral force and torque of precast bridge piers with loading displacement and rotation under compression-bending-shear-torsion loads. In existing technologies, the superposition effect of multiple deformation components under combined compression-bending-shear-torsion loads is ignored, resulting in insufficient accuracy in predicting the variation of lateral force and torque of bridge piers with loading displacement and rotation. This makes it difficult to provide reliable theoretical support for the cross-sectional design and reinforcement optimization of precast bridge piers, and easily leads to problems such as excessive reinforcement increasing costs or insufficient reinforcement causing safety hazards.

[0195] The above mainly describes the solutions of the embodiments of this application from the perspective of the method execution process. It is understood that, in order to achieve the above functions, the terminal includes the corresponding hardware structure and / or software modules for executing each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments provided herein, this application can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0196] This application embodiment can divide the terminal into functional units according to the above method example. For example, each function can be divided into a separate functional unit, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this application embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.

[0197] This application embodiment also provides a computer storage medium, wherein the computer storage medium stores a computer program for electronic data interchange, the computer program causing a computer to perform some or all of the steps of any of the load-deformation determination methods for precast bridge piers under compression, bending, shear and torsion as described in the above method embodiments.

[0198] This application also provides a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program that causes a computer to perform some or all of the steps of any of the load-deformation determination methods for precast bridge piers under compression, bending, shear, and torsion as described in the above method embodiments.

[0199] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0200] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0201] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical or other forms.

[0202] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0203] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software program module.

[0204] If the integrated unit is implemented as a software program module and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0205] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage device, which may include: a flash drive, a read-only memory, a random access memory, a magnetic disk, or an optical disk, etc.

[0206] The embodiments of this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion, characterized in that, include: The first model stage division and the first model analysis assumptions of the torque-rotation analysis model of precast bridge piers under compression, bending, shear and torsion are determined. Based on the first model stage division and the first model analysis assumptions, the torque and rotation of the critical point a, the torque and rotation of the critical point b and the torque and rotation of the critical point c in the elastic stage are calculated respectively. The second model stage division of the precast bridge pier shear force-displacement analysis model under compression-bending-shear-torsion action is determined. Based on the second model stage division and the second model analysis assumptions, the force and displacement at critical point A in the decompression stage, the force and displacement at critical point B in the yielding stage, and the force and displacement at critical point C in the degradation stage are calculated respectively. Connect the critical points o, a, b, and c of the torque-rotation angle analysis model to form a complete torque-rotation angle curve. Connect the critical points O, A, B, and C of the shear force-displacement analysis model to form a complete force-displacement curve. Construct a load-deformation analysis model for precast bridge piers based on the torque-rotation angle curve and the force-displacement curve. Precast bridge piers with different parameters were selected, and their torque-rotation curves and force-displacement curves were calculated using the load-deformation analysis model. The theoretical curves were compared with the experimental curves to verify the accuracy of the model's prediction of the load-deformation law of precast bridge piers.

2. The method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The first model analysis assumptions for determining the torque-rotation analysis model of precast bridge piers under compression-bending-shear-torsion loading include: Construct a spatial truss model for the bridge piers; In the spatial truss model of the bridge pier, the concrete is regarded as a diagonal compression member, the prestressed tendons are regarded as longitudinal reinforcement web members, and the stirrups are regarded as tension members. In the spatial truss model of the bridge pier, the concrete diagonal compression members only bear compression, not shear or tension. The lines of action of the resultant forces of the longitudinal reinforcement, stirrups, and diagonal compression members coincide; The role of the pins in the prestressing tendons is ignored; The torsional stiffness of the bridge pier is the series stiffness of each segment.

3. The method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The calculation of the torque and rotation angle at the critical point a of the elastic stage based on the stage division and analytical assumptions includes: Calculate the torque at the critical point a in the elastic stage based on the tensile strength of concrete and the section modulus of section oa in the elastic stage; Calculate the torsional stiffness of the precast pier at critical point a based on the shear modulus, moment of inertia of the section, and reduction factor. Calculate the rotation angle of the critical point a in the elastic stage based on the torsional stiffness at the critical point a and the torque at the critical point a in the elastic stage.

4. The method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion according to claim 3, characterized in that, The formula for calculating the torsional stiffness at point a is as follows: in, , Shear modulus Let the moment of inertia of the cross section be... Let be the reduction factor for point a, which is 0.

65.

5. The method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The calculation of the torque and rotation angle at critical point b based on the stage division and analytical assumptions includes: The torque at critical point b is calculated based on the torsional plastic modulus and ultimate shear stress of the precast pier joint section. Based on the stress generated by external forces in the reinforcement stage ab of the bridge pier spatial truss model, the torsional stiffness of the bridge pier in the reinforcement stage is calculated using the virtual work principle formula. The rotation angle at critical point b is calculated based on the torsional stiffness during the strengthening stage and the torque at critical point b.

6. The method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion according to claim 5, characterized in that, The formula for calculating the torsional stiffness during the strengthening stage is as follows: in, This refers to the torsional stiffness of a single segment of the bridge pier during the reinforcement stage. The sum of stresses generated by external forces, The stress generated by the unit torque, For the volume of the bridge pier, The elastic modulus of the bridge pier.

7. The method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The formulas for calculating the force and displacement at the critical point A are as follows: Let I be the force at critical point A, and I be the moment of inertia of the cross section. The width of the bridge pier segment. Calculate the height of the bridge piers. This is the initial tension force of the prestressing tendons. To apply the load to the upper part of the bridge pier, The cross-sectional area of ​​the bridge pier; in, The displacement of the critical point A. Let E be the curvature of the bridge pier, and E be the elastic modulus of the bridge pier. Let be the force at critical point A, I be the moment of inertia of the cross section, and h be the calculated height of the pier.

8. The method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The formulas for calculating the force and displacement at the critical point B are as follows: in, The force at critical point B, It is the vertical distance from the top of an in-plane crack parallel to the loading direction to the centroid of the pressure zone; The vertical distance from the top of the in-plane crack parallel to the loading direction to the centroid of the compression zone; The spacing between the stirrups. For the tensile force of the stirrups, The angle between a crack on a surface parallel to the loading direction and the direction along the pier height. The angle between the crack on the other side parallel to the loading direction and the direction along the pier height; in, The displacement of the critical point B. ρ is the elongation of the unbonded section of the prestressing tendon, D is the cross-sectional width, and c is the height of the compression zone. The force at critical point B, The stress distribution length of the prestressing tendon and yield strain The product of For bending stiffness, This refers to shear stiffness.

9. The method for determining the load-deformation of precast bridge piers under compression, bending, shear, and torsion according to claim 1, characterized in that, The method involves selecting precast bridge piers with different parameters, calculating their torque-rotation curves and force-displacement curves using the load-deformation analysis model, and comparing the theoretical curves with the experimental curves to verify the accuracy of the model's prediction of the load-deformation law of the precast bridge piers. This includes: The accuracy of the model is verified by comparing the positive load-deformation curve with the theoretically calculated curve.

10. A load-deformation determination system for precast bridge piers under compression, bending, shear, and torsion, characterized in that, include: The first determining unit is used to determine the first model stage division and the first model analysis assumptions of the torque-rotation analysis model of the precast bridge pier under compression, bending, shear and torsion. Based on the first model stage division and the first model analysis assumptions, the torque and rotation of the critical point a, the torque and rotation of the critical point b and the torque and rotation of the critical point c in the elastic stage are calculated respectively. The second determining unit is used to determine the second model stage division of the precast bridge pier shear force-displacement analysis model under compression-bending-shear-torsion action. Based on the second model stage division and the second model analysis assumptions, the force and displacement of critical point A in the decompression stage, the force and displacement of critical point B in the yielding stage, and the force and displacement of critical point C in the degradation stage are calculated respectively. The processing unit is used to connect the critical points o, a, b, and c of the torque-rotation angle analysis model to form a complete torque-rotation angle curve, and to connect the critical points O, A, B, and C of the shear force-displacement analysis model to form a complete force-displacement curve. Based on the torque-rotation angle curve and the force-displacement curve, a precast bridge pier load-deformation analysis model is constructed. The verification unit is used to select precast bridge piers with different parameters, calculate their torque-rotation curves and force-displacement curves using the load-deformation analysis model, and compare the theoretical curves with the experimental curves to verify the accuracy of the model's prediction of the load-deformation law of the precast bridge piers.

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