Shearing capacity calculation method and device and storage medium
By using nonlinear finite element analysis and stirrup dissipation tensile stress correction, the problem of overestimation of shear bearing capacity under vertical ground motion in existing bridge seismic design has been solved, enabling more accurate prediction and design of pier shear performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG UNIV OF TECH
- Filing Date
- 2026-02-27
- Publication Date
- 2026-05-15
AI Technical Summary
Existing bridge seismic design codes fail to account for the variable axial force effect when considering vertical ground motion, leading to an overestimation of the shear capacity of stirrups and an inability to accurately predict the shear performance of bridge piers. This makes them particularly prone to shear failure under strong vertical ground motion.
By establishing a nonlinear finite element analysis model, the relationship between the axial strain of the core concrete and the dissipated tensile stress of the stirrups is obtained, the calculation method of the stirrup shear bearing capacity is corrected, the lateral deformation and dynamic changes of the variable axial force caused by concrete compression are considered, and fiber beam-column elements and shear spring elements are coupled for modeling, and the evaluation is carried out in combination with the safety threshold index.
It significantly improves the accuracy of shear capacity calculation, is applicable to bridge design under near-fault and strong vertical earthquake action, and can be extended to the analysis of high piers, long-span bridges and complex superstructures. The calculation results are highly consistent with the measured values, providing a reliable design basis.
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Figure CN122046501A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of bridge seismic design and structural analysis technology, specifically to a method, equipment, and storage medium for calculating shear bearing capacity. Background Technology
[0002] Under strong vertical ground motion near a fault, the stress characteristics of reinforced concrete bridge piers differ significantly from those considering only horizontal ground motion. Extensive earthquake damage surveys show that bridges near the epicenter are prone to shear or flexural-shear failure of their piers under vertical pulses, exhibiting sudden and brittle failure characteristics that often lead to overall bridge instability or even collapse. Compared to horizontal ground motion, vertical ground motion not only causes a significant increase in the peak vertical acceleration of the structure but also results in drastic fluctuations in the axial force of the piers within a very short time, creating complex stress paths under cyclic tension and compression. Excessive axial compression or tension alters the internal force distribution of the piers, leading to increased nonlinear stress in the concrete core area and causing additional tensile strain on the stirrups, thus significantly reducing the actual shear capacity.
[0003] While current bridge seismic design codes incorporate a correction term for axial force on concrete shear capacity in their formulas, their theoretical basis primarily addresses static or constant axial compression conditions, failing to reflect the high-frequency variable axial force effect caused by vertical ground motion. These codes generally treat the contribution of stirrups as lateral restraint along the direction of diagonal cracks, assuming that stirrups always operate in the shear direction, neglecting the fact that the lateral expansion of concrete during compression causes radial tensile stress dissipation in the stirrups. With increasing axial compression, the Poisson effect of the core concrete intensifies, internal microcracks expand, and stirrups generate additional tensile strain to restrain lateral concrete deformation. The corresponding stress primarily balances the lateral expansion of concrete rather than directly contributing to shear resistance. Therefore, the effective shear capacity of stirrups is lower than the code-calculated value, especially under strong vertical ground motion; neglecting this effect leads to a systematic overestimation of shear capacity.
[0004] Vertical ground motion causes bridge piers to transition from bending failure to shear failure, a change that is difficult to predict using only macroscopic indicators (such as shear force or displacement). Traditional assessment methods based on macroscopic response cannot reveal the weakening mechanism of variable axial force on the shear performance of piers. To accurately describe the deterioration of shear performance under vertical ground motion, it is urgent to establish an improved shear capacity calculation method, supporting equipment, and storage medium that can reveal the coupling relationship between axial deformation of concrete and tensile stress of stirrups from the perspective of internal stress-strain mechanisms of structural members. This method should comprehensively consider the transverse deformation caused by concrete compression, the dissipated tensile stress of stirrups, and the dynamic variation law of variable axial force, thereby achieving accurate prediction of the shear performance of reinforced concrete bridge piers. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention provides a method, equipment, and storage medium for calculating shear bearing capacity, thus solving the problem of overestimating the shear strength of bridge piers in existing methods.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating shear bearing capacity, comprising the following steps:
[0007] Step 1: Obtaining the core concrete strain
[0008] Establish a nonlinear finite element analysis model of the bridge pier or obtain axial strain data at the centroid of the core concrete of the pier column by experimentally arranging strain gauges.
[0009] For numerical simulation, a coupled modeling approach using fiber beam-column elements and shear spring elements is adopted to capture the characteristics of coordinated bending and shear deformation.
[0010] Recorded core concrete axial strain As input parameters for subsequent calculations, they characterize the effect of axial force variation caused by vertical ground motion;
[0011] Step 2: Calculation of dissipative tensile stress in stirrups
[0012] Based on the Poisson relationship between the transverse and axial strains of concrete, the functional relationship between the dissipated tensile stress of the stirrups and the axial strain of the core concrete is derived:
[0013] ;
[0014] in, The elastic modulus of the steel reinforcement. Poisson's ratio for concrete For the axial strain of the core concrete, when the concrete is in a tensile state, =0;
[0015] Step 3: Correction of stirrup shear capacity
[0016] By introducing a dissipative tensile stress term into the formula for calculating the shear capacity of stirrups, the actual shear capacity of stirrups under variable axial force is obtained:
[0017] ;
[0018] in, The total area of the stirrups. The stirrup yield strength, d represents the stirrup spacing, and d represents the effective height of the cross-section;
[0019] Step 4: Calculation of Total Shear Capacity
[0020] The total shear capacity is defined as:
[0021] = + ;
[0022] in, The shear capacity of concrete, when the structure enters the shear failure stage, is simplified to... = ;
[0023] Step 5: Construction of Safety Thresholds and Performance Evaluation Indicators
[0024] Introducing safety threshold indicators Compared with the decrease in shear bearing capacity :
[0025] ;
[0026] in, To meet the shear resistance requirements under seismic loading, This represents the initial shear bearing capacity.
[0027] Preferably, the finite element model is established using dispBeamColumn elements, and the material constitutive model uses Concrete02 and Steel02.
[0028] Preferably, the shear spring unit adopts a degenerate "Pinching Limit-State" model to describe the degradation of shear stiffness and strength.
[0029] Preferably, the method is applicable to reinforced concrete bridge piers with circular cross-sections, rectangular cross-sections, and thin-walled hollow cross-sections.
[0030] Preferably, the method is embedded in bridge seismic design and analysis software to achieve real-time calculation of shear bearing capacity and performance visualization evaluation.
[0031] Preferably, the safety threshold Compared with the decline Used as a criterion for pier shear failure, among which =0 indicates that the structure has undergone shear failure.
[0032] Preferably, the calculation results of the method can be compared with current standards (ACI 318, AASHTO, Caltrans, JTGD60-2018, etc.) to correct the shear design factor and establish a new shear design criterion.
[0033] Preferably, the implementation method is not only applicable to bridge pier structures under near-fault vertical seismic motion, but can also be extended to the seismic vulnerability analysis of high-pier, long-span bridges and bridges with complex superstructures.
[0034] The present invention also provides a shear bearing capacity calculation device, the shear bearing capacity calculation device including a processor, a memory, and a shear bearing capacity calculation program stored in the memory and executable by the processor, wherein when the shear bearing capacity calculation program is executed by the processor, the steps of the above-described shear bearing capacity calculation method are implemented.
[0035] The present invention also provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores a shear bearing capacity calculation program, which, when executed by a processor, implements the steps of the above-described shear bearing capacity calculation method.
[0036] Beneficial effects
[0037] This invention provides a method, apparatus, and storage medium for calculating shear bearing capacity. Compared with existing technologies, it has the following advantages:
[0038] (1) The shear bearing capacity calculation method, equipment and storage medium, by introducing the concept of stirrup dissipation tensile stress, establishes for the first time the quantitative relationship between stirrup stress dissipation and core concrete axial strain, which significantly improves the accuracy of shear bearing capacity calculation and avoids the overestimation error that is common in existing specifications;
[0039] Secondly, this method fully considers the variable axial force effect caused by vertical ground motion, making it more widely applicable. It is suitable for the seismic design of reinforced concrete bridge piers in near-fault areas and under strong vertical earthquake action, and can also be extended to the seismic vulnerability analysis of high piers, long-span bridges and bridges with complex superstructures.
[0040] (2) The shear bearing capacity calculation method, equipment and storage medium have a clear calculation process and well-defined parameters. They are compatible with the existing bridge seismic design code. The calculation results can be compared with the current code to correct the design coefficient or establish new criteria.
[0041] The computer program stored on the storage medium is embedded in the bridge seismic analysis and design software, which realizes automated calculation, real-time evaluation and performance visualization of shear performance, providing reliable theoretical basis and technical support for bridge seismic design. The calculation results are highly consistent with the measured values after being verified by the variable axial force quasi-static test and shaking table test. The prediction accuracy and applicability are better than the empirical formulas of traditional design codes, which have good engineering promotion value and theoretical innovation significance. Attached Figure Description
[0042] Figure 1 This is a flowchart illustrating the invention process;
[0043] Figure 2 This is a schematic diagram of the finite element model of the pier column;
[0044] Figure 3This is a schematic diagram showing the stress on the core concrete and stirrups in a circular cross-section.
[0045] Figure 4 This invention presents a comparison of fiber strain under horizontal ground motion only and coupled horizontal and vertical ground motion at the column top, middle, and bottom sections in an embodiment of the present invention.
[0046] Figure 5 For only horizontal ground motion and the coupling effect of horizontal and vertical ground motion and Indicator comparison;
[0047] Figure 6 This is a schematic diagram of the hardware structure of the shear bearing capacity calculation device involved in the embodiments of this application. Detailed Implementation
[0048] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0049] Please see Figure 1-6 This application provides a method for calculating shear bearing capacity, the specific operation of which is as follows:
[0050] S1, Objects and Targets
[0051] A shaking table test of an existing circular cross-section RC column was selected as the object (the column base is fixed, and a rigid block at the top simulates the mass and moment of inertia of the superstructure). The goal is to numerically reproduce the differences between the overall response of the component and the layered response of the cross-section material under two inputs: "horizontal ground motion only (X)" and "horizontal + vertical ground motion (X + Z)". Specifically, the shear bearing capacity obtained using the method of this invention will be calculated and compared. The time-history relationship with shear requirements and the safety threshold Bearing capacity reduction ratio The differences will be analyzed to verify the effectiveness of the method under vertical loading. To achieve this, a fiber beam-column element model considering shear deformation will be built in OpenSees. The axial strain at the centroid of the core concrete will be recorded using the command recorder Element-ele $Tagsection $SecNumfiber $y $zstressStrain. ,Will Substituting into the formula, we obtain the dissipated tensile stress of the stirrups, and then utilize... and Calculate the actual shear bearing capacity;
[0052] S2, Modeling and Parameters
[0053] In OpenSees, a nonlinear model of fiber beam-column + shear spring series was established: the beam-column element was dispBeamColumn fiber element (4 integration points), the length of the end element was taken as about 0.7 times the diameter of the pier column circular section to better capture the plastic hinge, the concrete was Concrete02 and the steel reinforcement was Steel02, and the section was refined and discretized along the circumferential and radial directions to accurately define the core area and the protective layer.
[0054] A zero-length shear spring is set at the bottom of the shear spring column. The material adopts the Pinching Limitstate model to characterize the shear strength degradation and stiffness degradation. At the same time, an equivalent rotational spring is set at the bottom to reflect the influence of rigid body rotation caused by the flexibility of the loading system.
[0055] Top mass and moment of inertia: The rigid block and the top of the column are connected by rigidLink, which concentrates the equivalent mass and moment of inertia of the superstructure at the center of mass of the rigid block, and applies the vertical mass degree of freedom to participate in the inertial force when considering the vertical component;
[0056] Earthquake input: The Northridge ground motion (RSN 1051) (horizontal and vertical components) recorded by the PacoimaDam station was used. The data was processed to ensure consistency in terms of test scale and amplitude, so that the two sets of working conditions "X" and "X+Z" are comparable in the strong plastic zone.
[0057] S3. Fiber Strain Extraction and Calculation
[0058] The axial strain time history of the centroid and core boundary fiber of the section is recorded using the recorder Element-ele $idsection $ipfiber $y $zstressStrain. (t), when When (t) > 0 (under pressure), substitute into The time history of the dissipated tensile stress of the stirrups is obtained when When (t) ≤ 0, let =0, therefore, the shear capacity of the stirrups is adjusted accordingly: and with (t) superimposed to obtain (t) = (t)+ (t) (can be taken after shear failure) ≈ );
[0059] S4. Results and Judgments
[0060] Numerical reproduction shows that the two sets of working conditions have limited differences in macroscopic indicators such as shear force and inter-story displacement, but the peak values of axial force and axial strain in the core area are significantly different. The "X+Z" working condition reaches its peak earlier and exhibits greater compressive strain, thus producing greater [results]. ,make and All showed a more significant decrease. Near similar peak shear demand, the "X+Z" condition triggered the shear failure criterion earlier than the "X" condition. The time to drop to 0 is earlier, after shear failure. The peak value is also significantly larger, proving that this method is more sensitive to shear degradation caused by vertically induced axial force, and can reasonably explain the experimental phenomenon that the results of shear force and horizontal displacement are similar but the failure mechanisms are different.
[0061] This application provides a shear bearing capacity calculation device, which can be a personal computer (PC), laptop computer, server or other device with data processing capabilities.
[0062] Reference Figure 6 , Figure 6 This is a schematic diagram of the hardware structure of the shear bearing capacity calculation device involved in the embodiments of this application. In the embodiments of this application, the shear bearing capacity calculation device may include a processor, a memory, a communication interface, and a communication bus.
[0063] The communication bus can be of any type and is used to interconnect the processor, memory, and communication interface.
[0064] The communication interface includes input / output (I / O) interfaces, physical interfaces, and logical interfaces, which are used to realize the interconnection of devices within the AAAA device, as well as interfaces for realizing the interconnection of the AAAA device with other devices (such as other computing devices or user devices). The physical interface can be an Ethernet interface, a fiber optic interface, an ATM interface, etc., and the user device can be a display screen, a keyboard, etc.
[0065] Memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.
[0066] The processor can be a general-purpose processor. The general-purpose processor can call the shear bearing capacity calculation program stored in the memory and execute the shear bearing capacity calculation method provided in the embodiments of this application. For example, the general-purpose processor can be a central processing unit (CPU). The method executed when the shear bearing capacity calculation program is called can refer to the embodiments of the shear bearing capacity calculation method of this application, which will not be repeated here.
[0067] Those skilled in the art will understand that Figure 6 The hardware structure shown does not constitute a limitation of this application and may include more or fewer components than shown, or combine certain components, or have different component arrangements.
[0068] This application also provides a computer-readable storage medium.
[0069] The computer-readable storage medium of this application stores a shear bearing capacity calculation program, wherein when the shear bearing capacity calculation program is executed by a processor, it implements the steps of the shear bearing capacity calculation method described above.
[0070] The method implemented when the shear bearing capacity calculation program is executed can be referred to the embodiment of the shear bearing capacity calculation method of this application, and will not be repeated here.
Claims
1. A method for calculating shear bearing capacity, characterized in that, Includes the following steps: Step 1: Obtaining the core concrete strain Establish a nonlinear finite element analysis model of the bridge pier or obtain axial strain data at the centroid of the core concrete of the pier column by experimentally arranging strain gauges. For numerical simulation, a coupled modeling approach using fiber beam-column elements and shear spring elements is adopted to capture the characteristics of coordinated bending and shear deformation. Recorded core concrete axial strain As input parameters for subsequent calculations, they characterize the effect of axial force variation caused by vertical ground motion; Step 2: Calculation of dissipative tensile stress in stirrups Based on the Poisson relationship between the transverse and axial strains of concrete, the functional relationship between the dissipated tensile stress of the stirrups and the axial strain of the core concrete is derived: ； in, The elastic modulus of the steel reinforcement. Poisson's ratio for concrete For the axial strain of the core concrete, when the concrete is in a tensile state, =0; Step 3: Correction of stirrup shear capacity By introducing a dissipative tensile stress term into the formula for calculating the shear capacity of stirrups, the actual shear capacity of stirrups under variable axial force is obtained: ； in, The total area of the stirrups. The stirrup yield strength, d represents the stirrup spacing, and d represents the effective height of the cross-section; Step 4: Calculation of Total Shear Capacity Total shear capacity is defined as: = + ； in, The shear capacity of concrete, when the structure enters the shear failure stage, is simplified to... = ; Step 5: Construction of Safety Thresholds and Performance Evaluation Indicators Introducing safety threshold indicators Compared with the decrease in shear bearing capacity : ； in, To meet the shear resistance requirements under seismic loading, This represents the initial shear bearing capacity.
2. The method for calculating shear bearing capacity according to claim 1, characterized in that: The finite element model is established using dispBeamColumn elements, and the material constitutive model uses Concrete02 and Steel02.
3. The method for calculating shear bearing capacity according to claim 1, characterized in that: The shear spring unit adopts a degenerate "Pinching Limit-State" model to describe the degradation of shear stiffness and strength.
4. The method for calculating shear bearing capacity according to claim 1, characterized in that: The method is applicable to reinforced concrete bridge piers with circular cross-sections, rectangular cross-sections, and thin-walled hollow cross-sections.
5. The method for calculating shear bearing capacity according to claim 1, characterized in that: The method is embedded in bridge seismic design and analysis software to achieve real-time calculation of shear bearing capacity and performance visualization evaluation.
6. The method for calculating shear bearing capacity according to claim 1, characterized in that: The safety threshold Compared with the decline Used as a criterion for shear failure of pier columns, among which =0 indicates that the structure has undergone shear failure.
7. A method for calculating shear bearing capacity according to any one of claims 1-6, characterized in that: The calculation results obtained by the method can be compared with the current specifications to revise the shear design factor and establish new shear design criteria.
8. A method for calculating shear bearing capacity according to any one of claims 1-6, characterized in that: The method is not only applicable to bridge pier structures subjected to near-fault vertical ground motion, but can also be extended to the seismic vulnerability analysis of high-pier, long-span bridges and bridges with complex superstructures.
9. A shear bearing capacity calculation device, characterized in that, The shear bearing capacity calculation device includes a processor, a memory, and a shear bearing capacity calculation program stored in the memory and executable by the processor, wherein when the shear bearing capacity calculation program is executed by the processor, it implements the steps of the shear bearing capacity calculation method as described in any one of claims 1 to 8.
10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a shear bearing capacity calculation program, which, when executed by a processor, implements the steps of a shear bearing capacity calculation method according to any one of claims 1 to 8.