A method for identifying the dual modulus of materials in bridge span structures based on single-beam static load tests.

Abstract

This invention discloses a method for identifying the dual modulus of materials in bridge structures based on a single-beam static load test, belonging to the field of material mechanical property testing. The method includes: selecting a precast beam of the bridge structure simply supported on supports; applying a concentrated static load perpendicular to the beam axis at the top mid-span of the precast beam; collecting the top strain, bottom strain, mid-span deflection, and support displacement of the precast beam's mid-span section; and simultaneously solving for the tensile and compressive moduli of the material based on a dual-modulus mechanical model using the collected strain, deflection, load values, span, and cross-sectional geometric parameters. This invention can simultaneously and accurately identify the tensile and compressive moduli of materials through a single static load test, eliminating the systematic errors introduced by the discreteness of the specimens in traditional separate tests. The test results closely match the service condition of actual bridge beams, and are characterized by simple operation, high efficiency, and reliable results, making it suitable for material property testing of precast beams in bridge engineering.

Description

Technical Field

[0001] This invention belongs to the field of material mechanical property testing technology, and particularly relates to a method for identifying the dual modulus of materials in bridge structures based on a single beam static load test. Background Technology

[0002] In the fields of materials mechanical property testing and engineering structure inspection, accurately obtaining the elastic modulus of materials is crucial for structural design and safety assessment. Currently, existing technologies mainly fall into two categories to address the situation where materials may exhibit different elastic moduli under tension and compression (i.e., bimodal characteristics). The first category is the traditional single-modulus testing method, which is the most widely used. This method is based on classical beam bending theory, assuming that the material has the same elastic modulus in the tension and compression zones. Through three- or four-point static bending tests on a single standard beam specimen, the deflection or strain of the specimen is measured. Substituting this into the Euler-Bernoulli beam formula based on the single-modulus assumption, a comprehensive "bending modulus" is calculated. This method is simple to operate and has a standardized testing procedure. For example, the plastic bending performance testing methods specified in standards such as ASTM D790 or GB / T 9341 adopt this principle, demonstrating high testing efficiency and a wide range of applications in engineering practice. The second type is the separate bimodulus testing method. For materials with significant differences in tensile and compressive moduli, existing technologies prepare independent tensile and compressive specimens separately, and then use equipment such as universal testing machines to conduct uniaxial tensile and compressive tests to obtain the tensile and compressive moduli of the material separately. Theoretically, this method can directly measure the tensile and compressive moduli, providing a technical path for understanding the bimodal characteristics of materials.

[0003] However, the aforementioned existing technologies still have significant shortcomings in practical applications. For traditional single-modulus testing methods, the core flaw lies in the simplification of the mechanical model and the deviation from physical reality. Because this method presupposes equal tensile and compressive moduli, the test results are merely a weighted average of the tensile and compressive moduli in a physical sense, failing to decouple and separately output the material's true tensile and compressive moduli. When the tensile and compressive moduli of materials (such as concrete, some composite materials, and rocks) differ significantly, the test results will deviate severely from the material's true mechanical behavior under pure tension or pure compression, thus introducing non-negligible errors in structural design and numerical simulation. For the separated dual-modulus testing method, its shortcomings mainly lie in the consistency of specimens, the matching of stress states, and testing efficiency. First, this method relies on two physically independent specimens. Due to the inherent heterogeneity of the material, even specimens taken from the same parent material will have difficult-to-identify internal microstructures, resulting in systematic errors that cannot be eliminated, leading to significant dispersion in the test results. Secondly, the stress fields generated inside the specimen in uniaxial tensile and uniaxial compression tests are fundamentally different from the complex stress states of materials in actual bending members, where tensile and compressive stresses exist simultaneously. Simply combining the modulus values ​​obtained under different stress states makes it difficult to accurately reflect the overall mechanical response of the material under bending stress. Furthermore, this method requires two different sets of testing equipment and procedures, resulting in long testing cycles and high costs. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a method for identifying the dual modulus of materials in bridge span structures based on a single-beam static load test, thereby resolving the issues present in the prior art.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for identifying the dual modulus of materials in bridge span structures based on a single-beam static load test, comprising: A precast beam of the bridge span structure was selected as the test specimen, and the precast beam was simply supported on two supports. A single-point concentrated static load perpendicular to the beam axis is applied at the top mid-span of the precast beam; The top strain, bottom strain, mid-span deflection, and support displacement of the precast beam mid-span section were collected. Based on the collected top strain, bottom strain, mid-span deflection, single-point concentrated static load value, span and cross-sectional geometric parameters of the precast beam, the tensile elastic modulus and compressive elastic modulus of the material are solved simultaneously using a dual-modulus mechanical model.

[0006] Preferably, the precast beam is any one of a hollow slab, a T-beam, or a small box girder, and the ratio of the span to the section height of the precast beam is greater than 15.

[0007] Preferably, the process of applying a single-point concentrated static load perpendicular to the beam axis includes: The load is applied by a single-point centralized loading device at mid-span, which includes a reaction frame, jacks, load sensors, and distribution beams.

[0008] Preferably, the top strain and the bottom strain are acquired by a strain acquisition unit, which includes five strain sensors, respectively attached to each of the quarter points from the top to the bottom of the mid-span section of the precast beam.

[0009] Preferably, the mid-span deflection and support displacement are collected by a deflection acquisition unit, which includes three displacement gauges, respectively installed at the bottom of the mid-span of the precast beam and at the two supports.

[0010] Preferably, the process of simultaneously solving for the tensile and compressive moduli of the material includes: The position of the neutral axis is determined based on the top strain, the bottom strain, and the cross-sectional height of the precast beam. The measured section stiffness is determined based on the mid-span deflection, the load value, and the span. Based on the neutral axis position and the measured cross-sectional stiffness, the tensile modulus and the compressive modulus are calculated.

[0011] Preferably, when the precast beam is a rectangular cross-section beam, the formulas for solving the tensile modulus of elasticity and the compressive modulus of elasticity are: ; ; Where P is the load value, L is the span, f is the mid-span deflection, b is the cross-sectional width, and h is the cross-sectional width. c h is the height of the compression zone of the cross section. t The height of the tension zone of the cross section is given by E, where n is the ratio of the elastic moduli under tension and compression. c For compressive elastic modulus, E t This refers to the tensile modulus of elasticity.

[0012] Preferably, when the precast beam is a T-shaped or I-shaped cross-section beam, the tensile modulus and compressive modulus are solved simultaneously by introducing the position parameter of the neutral axis located within the web and combining the cross-sectional geometric parameters with the measured cross-sectional stiffness.

[0013] Preferably, the solution is performed by a data processing unit with a pre-set iterative solution program. The iterative solution program outputs the tensile elastic modulus and the compressive elastic modulus based on the top strain, the bottom strain, the mid-span deflection, the load value, the span, and the cross-sectional geometric parameters using an iterative algorithm.

[0014] In a second aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any of the first aspects.

[0015] Compared with the prior art, the present invention has the following advantages and technical effects: This invention applies a concentrated static load at a single point in the mid-span of a precast bridge beam during a single static load test, simultaneously collecting data on the top strain, bottom strain, mid-span deflection, and support displacement at the mid-span section. Using multi-source data from the same specimen, under the same loading and stress field, and combined with a dual-modulus mechanical model, the tensile and compressive moduli of the material are simultaneously derived. This technique avoids the cumbersome process of separate tensile and compressive tests required by traditional methods, eliminates the need for preparing independent specimens or changing loading equipment, significantly shortens the testing cycle, and reduces testing costs.

[0016] This invention uses precast beams (hollow slabs, T-beams, and small box girders) specifically designed for bridge engineering as test objects, and applies a concentrated static load at a single point mid-span under simply supported boundary conditions. The specimen form, constraint conditions, and loading method are consistent with the stress characteristics of actual bridge beams under service conditions. Compared to traditional methods that use small-sized standard specimens or non-bridge components, the test results of this invention can directly reflect the bimodal characteristics of bridge materials under actual bending stress, providing more accurate material constitutive input parameters for bridge structural design, safety assessment, and finite element analysis.

[0017] This invention requires data collection from only five key measuring points: strain at the top of the mid-span, strain at the bottom of the mid-span, deflection at the mid-span, and displacement at the support points. This streamlined measuring point combination minimizes the number of sensors and data acquisition channels while maintaining the accuracy of the bimodal calculation, reducing the operational complexity and equipment cost of on-site testing, making it particularly suitable for on-site testing environments in bridge engineering.

[0018] This method has the advantages of universal equipment, simple operation, and controllable cost, making it easy to promote and apply on a large scale in university laboratories, testing institutions, and engineering sites. Attached Figure Description

[0019] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of a rectangular cross-section according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a T-shaped cross-section according to an embodiment of the present invention; Figure 3 This is a schematic diagram of an I-shaped cross-section according to an embodiment of the present invention; Figure 4 This is a flowchart illustrating the calculation process of an embodiment of the present invention; Figure 5 This is a schematic diagram of a single-beam static load test structure according to an embodiment of the present invention. Detailed Implementation

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0022] Example 1 This embodiment provides a method for identifying the dual modulus of materials in bridge span structures based on single-beam static load tests, including: Step 1: Select a precast beam of the bridge span structure as a test specimen and simply support the precast beam on two supports; Furthermore, the precast beam is any one of a hollow slab, a T-beam, or a small box girder, and the ratio of the span to the section height of the precast beam is greater than 15.

[0023] Specifically, precast beams are used in the bridge structure, including but not limited to hollow slabs, T-beams, and small box girders. The ratio of the beam's span L to its section height h is greater than 15, i.e., L / h > 15, to ensure that the influence of shear deformation on normal strain is less than the allowable error range in the project.

[0024] Step 2: Apply a single-point concentrated static load perpendicular to the beam axis at the top mid-span of the precast beam; Furthermore, the process of applying a single-point concentrated static load perpendicular to the beam axis includes: The load is applied by a single-point centralized loading device at mid-span, which includes a reaction frame, jacks, load sensors, and distribution beams.

[0025] Specifically, a single-point centralized loading device is adopted at mid-span, including a reaction frame, jacks, load sensors, and distribution beams. The loading point is located at the top of the mid-span of the beam, and the load direction is perpendicular to the longitudinal axis of the beam, forming a single bending moment distribution area.

[0026] Step 3: Collect the top strain, bottom strain, mid-span deflection, and support displacement of the precast beam at the mid-span section; Furthermore, the top strain and the bottom strain are acquired by a strain acquisition unit, which includes five strain sensors, respectively attached to each of the quarter points from the top to the bottom of the mid-span section of the precast beam.

[0027] Specifically, strain sensors are arranged symmetrically along the longitudinal axis of the beam, and the measurement data is used to determine the cross-sectional strain gradient.

[0028] Furthermore, the mid-span deflection and support displacement are collected by a deflection acquisition unit, which includes three displacement gauges, respectively installed at the bottom of the mid-span of the precast beam and at the two supports.

[0029] Specifically, the deflection displacement gauge is used to measure mid-span deflection. f。

[0030] In this embodiment, as Figure 5 As shown, the loading unit acts on the top of the beam at mid-span via a jack; the two ends of the beam are simply supported by supports; the displacement gauge rod is in contact with the bottom of the beam; and the strain sensor is attached to the surface of the beam.

[0031] Step 4: Based on the collected top strain, bottom strain, mid-span deflection, single-point concentrated static load value, span and cross-sectional geometric parameters of the precast beam, simultaneously solve the tensile elastic modulus and compressive elastic modulus of the material using a dual-modulus mechanical model.

[0032] Furthermore, the process of simultaneously solving for the tensile and compressive moduli of the material includes: determining the position of the neutral axis based on the top strain, the bottom strain, and the cross-sectional height of the precast beam; determining the measured cross-sectional stiffness based on the mid-span deflection, the load value, and the span; and solving for the tensile and compressive moduli based on the position of the neutral axis and the measured cross-sectional stiffness.

[0033] Furthermore, the solution is obtained by a data processing unit with a pre-set iterative solution program. The iterative solution program outputs the tensile elastic modulus and compressive elastic modulus based on the top strain, the bottom strain, the mid-span deflection, the load value, the span, and the cross-sectional geometric parameters using an iterative algorithm.

[0034] Furthermore, such as Figure 1 As shown, when the precast beam is a rectangular cross-section beam, the cross-sectional geometric parameter is the cross-sectional width. b Cross-sectional height h， Based on the measured strains at the top and bottom of the cross-section, we can obtain: ; And from , .

[0035] Mid-span deflection under concentrated load P: ; In the formula: .

[0036] The formulas for solving the tensile modulus of elasticity and the compressive modulus of elasticity are: ; ; Where P is the load value, L is the span, f is the mid-span deflection, b is the cross-sectional width, and h is the cross-sectional width. c h is the height of the compression zone of the cross section. t The height of the tension zone of the cross section is given by E, where n is the ratio of the elastic moduli under tension and compression. c For compressive elastic modulus, E t This refers to the tensile modulus of elasticity.

[0037] Furthermore, when the precast beam is a T-shaped or I-shaped cross-section beam, the tensile modulus and compressive modulus are solved simultaneously by introducing the position parameter of the neutral axis located within the web and combining the cross-sectional geometric parameters with the measured cross-sectional stiffness.

[0038] Specifically, such as Figure 2 As shown, when the precast beam is a T-shaped cross-section beam, the cross-sectional geometric parameters include the flange width. b 2. Flange height h 2. Web height h 1. Web width b 1. Based on the measured strain at the top and bottom of the cross-section, we can obtain: ; And from , .

[0039] Mid-span deflection under concentrated load P: ; In the formula: (The neutral axis is located within the web).

[0040] From the above formula, we can obtain: ; ; Where P is the load value, L is the span, f is the mid-span deflection, b1 is the web width, hc is the height of the compression zone of the section, n is the ratio of elastic modulus under tension and compression, b2 is the flange width, h1 is the web height, h2 is the flange height, Ec is the compressive elastic modulus, and Et is the tensile elastic modulus.

[0041] like Figure 3 As shown, when the precast beam is an I-shaped cross-section beam, the cross-sectional geometric parameters include the width of the top plate. b d Top plate thickness h d Base plate width b b Base plate thickness h b Web height h w Total web thickness b w Based on the measured strains at the top and bottom of the cross-section, we can obtain: ; And from , .

[0042] Mid-span deflection under concentrated load P: ; In the formula: (The neutral axis is located within the web).

[0043] From the above formula, we can obtain: ; ; Where P is the load value, L is the span, f is the mid-span deflection, bb is the bottom plate width, hb is the bottom plate thickness, n is the ratio of elastic modulus under tension and compression, bw is the total thickness of the web, hw is the web height, bd is the top plate width, hd is the top plate thickness, Ec is the compressive elastic modulus, and Et is the tensile elastic modulus.

[0044] When the precast beam is a beam with a general cross-section, based on the measured strain at the top and bottom of the cross-section, we can obtain: ; And the concentrated load at mid-span P Mid-span measured deflection f The measured cross-sectional stiffness can be obtained. D 实 = PL 3 / 48 f ; Combination D 实 , h c Using a self-developed program and an iterative solution method, the elastic modulus under bending, tension, and compression states can be calculated. E t ,E c The computer has a pre-installed iterative solution program for cross-sectional characteristic parameters that considers dual moduli. The specific solution flowchart is shown below. Figure 4 As shown.

[0045] In this embodiment, the strain sensor and deflection gauge are connected to the data acquisition instrument via signal lines; the data acquisition instrument is connected to the computer via a communication interface; the computer's pre-installed iterative solution program processes the acquired strain signal, deflection signal, and load signal, and outputs E. t E c value.

[0046] The beneficial effects of this embodiment: To address the problems of inaccurate identification of the tensile and compressive moduli of materials through a single test, discrepancies in results due to specimen inconsistencies, and low testing efficiency in existing technologies, this invention aims to provide a dual-modulus identification method for bridge structures based on single-beam static load tests. This method aims to overcome the inherent defects in the mechanical model of traditional single-modulus testing methods and the inconsistencies in specimen structure and loading methods of separate testing methods. By using single-beam components of bridges (hollow slabs, T-beams, small box girders), under a concentrated load applied at mid-span, and comprehensively utilizing multi-point response data of deflection and strain at key sections such as mid-span and quarter-span, combined with a mechanical analysis model that reflects the difference in tensile and compressive moduli, the invention achieves synchronous and accurate inversion of the tensile and compressive elastic moduli of the material. This invention not only decouples and separately determines the dual-modulus values ​​of the material from a physical mechanism perspective, but also avoids systematic errors introduced by specimen differences, significantly improving the accuracy and consistency of test results, while simplifying the testing process and increasing experimental efficiency.

[0047] The material dual-modulus identification method for bridge span structures based on single-beam static load tests has the core advantage of simultaneously and accurately determining the elastic modulus Et and Ec of the material under bending, tension, and compression states in a single test. Compared with traditional methods, this embodiment shows significant improvements in theoretical rigor, testing efficiency, and result reliability. Specific advantages and positive effects are as follows: ①Simultaneous measurement and high efficiency and convenience; Traditional methods typically require obtaining the compressive modulus through compression testing, followed by obtaining the tensile modulus using the Brazilian disc splitting test or direct tensile testing. This process is not only cumbersome but also prone to introducing additional errors due to variations in specimens and loading conditions. This new method, however, requires only a single static load test on a single beam (mid-span loading). By measuring the beam's strain response in the pure bending segment, both the flexural tensile and compressive elastic moduli of the material can be identified simultaneously. This significantly simplifies the testing process, shortens the testing cycle, and reduces testing costs.

[0048] ② The results are highly accurate and reliable; Traditional four-point bending tests for beams establish a pure bending zone at mid-span, free from shear stress interference, ensuring that the stress-strain distribution in this section strictly conforms to the plane section assumption. For single beams (hollow slabs, T-beams, small box girders) in bridge structures, the span-to-height ratio is typically greater than 15. According to Timoshenko's beam theory, for a simply supported beam with a span-to-height ratio of 15, the additional deflection caused by shear force usually accounts for no more than 3% of the total deflection, resulting in a nonlinear error in the cross-sectional normal strain that is far less than the allowable range for engineering measurements. Combined with recent research, under a concentrated load P at mid-span, shear has no effect on the bending normal stress in a simply supported beam; the stress-strain distribution in the cross-section strictly conforms to the plane section assumption. In summary, the four-point bending test loading method is relatively complex, and it is difficult to ensure that the two loading points are completely symmetrical and consistent. However, by combining high-precision strain measurement techniques (such as strain gauges or digital image correlation technology), accurate data on the neutral layer location and the tensile and compressive strain at the top and bottom surfaces of the beam can be obtained. Based on these precise mechanical responses, substituting them into the bimodulus theoretical model for inversion calculations can significantly improve the accuracy of the identification results. Studies have shown that optimizing the test configuration can reduce the test error of the compressive modulus from 30% to 5%.

[0049] ③ The theoretical model has strong compatibility; This identification method can be combined with advanced material constitutive models (such as the Latorre-Montáns model based on strain energy functions) to handle materials with four independent elastic parameters (tensile modulus, compressive modulus, tensile Poisson's ratio, and compressive Poisson's ratio). This makes the method applicable not only to traditional single-modulus materials but also to novel materials with significant tensile-compressive modulus inequality, such as concrete, rock, ceramics, and graphite.

[0050] ④ High value for engineering application and promotion; Static load testing is one of the most fundamental and mature methods in materials and structural testing. This embodiment is based on standard beam components of bridge span structures, eliminating the need for developing complex specialized fixtures or testing equipment, and is easily implemented in conventional materials mechanics laboratories. The identified bimodal parameters can provide more accurate material constitutive inputs for precision mechanical design, civil engineering structural design, and finite element analysis of complex components, thereby improving the accuracy of simulation analysis and engineering design.

[0051] Example 2 This embodiment also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0052] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for identifying the dual modulus of materials in bridge span structures based on single-beam static load tests, characterized in that, Includes the following steps: A precast beam of the bridge span structure was selected as the test specimen, and the precast beam was simply supported on two supports. A single-point concentrated static load perpendicular to the beam axis is applied at the top mid-span of the precast beam; The top strain, bottom strain, mid-span deflection, and support displacement of the precast beam mid-span section were collected. Based on the collected top strain, bottom strain, mid-span deflection, single-point concentrated static load value, span and cross-sectional geometric parameters of the precast beam, the tensile elastic modulus and compressive elastic modulus of the material are solved simultaneously using a dual-modulus mechanical model.

2. The method according to claim 1, characterized in that, The precast beam is any one of hollow slab, T-beam or small box girder, and the ratio of the span to the section height of the precast beam is greater than 15.

3. The method according to claim 1, characterized in that, The process of applying a concentrated static load at a single point perpendicular to the beam axis includes: The load is applied by a single-point centralized loading device at mid-span, which includes a reaction frame, jacks, load sensors, and distribution beams.

4. The method according to claim 1, characterized in that, The top strain and the bottom strain are collected by a strain acquisition unit, which includes five strain sensors, respectively attached to each of the four quarter points from the top to the bottom of the mid-span section of the precast beam.

5. The method according to claim 1, characterized in that, The deflection at mid-span and the displacement at the support are collected by a deflection acquisition unit, which includes three displacement gauges, respectively installed at the bottom of the mid-span of the precast beam and at the two supports.

6. The method according to claim 1, characterized in that, The process of simultaneously solving for the tensile and compressive moduli of a material includes: The position of the neutral axis is determined based on the top strain, the bottom strain, and the cross-sectional height of the precast beam. The measured section stiffness is determined based on the mid-span deflection, the load value, and the span. Based on the neutral axis position and the measured cross-sectional stiffness, the tensile modulus and the compressive modulus are calculated.

7. The method according to claim 6, characterized in that, When the precast beam is a rectangular cross-section beam, the formulas for solving the tensile modulus of elasticity and the compressive modulus of elasticity are: ； ； Where P is the load value, L is the span, f is the mid-span deflection, b is the cross-sectional width, and h is the cross-sectional width. c h is the height of the compression zone of the cross section. t The height of the tension zone of the cross section is given by E, where n is the ratio of the elastic moduli under tension and compression. c For compressive elastic modulus, E t This refers to the tensile modulus of elasticity.

8. The method according to claim 6, characterized in that, When the precast beam is a T-shaped or I-shaped cross-section beam, the tensile modulus and compressive modulus are solved simultaneously by introducing the position parameter of the neutral axis located in the web and combining the cross-sectional geometric parameters and the measured cross-sectional stiffness.

9. The method according to claim 1, characterized in that, The solution is obtained by a data processing unit with a pre-set iterative solution program. The iterative solution program outputs the tensile elastic modulus and the compressive elastic modulus based on the top strain, the bottom strain, the mid-span deflection, the load value, the span, and the cross-sectional geometric parameters using an iterative algorithm.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-9.

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