Method for calculating stiffness degradation rule of hogging moment region of steel-concrete composite beam and storage medium

Abstract

The invention provides a steel-concrete composite beam hogging moment region rigidity degradation rule calculation method and a storage medium, and belongs to the technical field of computer-aided calculation. The method comprises the following steps of S100, determining random fatigue loads borne by a hogging moment area of the steel-concrete composite beam, and calculating the amplitude S and the amplitude distribution rule of each fatigue load; s200, performing curve fitting on the amplitude distribution rule of the fatigue load, and determining a probability density function of the amplitude of the fatigue load; s300, determining the fatigue life of the hogging moment area of the steel-concrete composite beam; s400, the static load ultimate bearing bending moment of the hogging moment area of the steel-concrete composite beam is determined; s500, determining a rigidity reduction value of the hogging moment area of the steel-concrete composite beam during fatigue failure; and S600, calculating the rigidity degradation rule of the steel-concrete composite beam under the random fatigue load. According to the method, the rigidity degradation process of the hogging moment area of the steel-concrete composite beam can be calculated and predicted in advance, and a theoretical basis is provided for maintenance and repair of a bridge.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided computing technology, and more specifically, it relates to a method and storage medium for calculating the stiffness degradation law in the negative bending moment zone of steel-concrete composite beams. Background Technology

[0002] In recent years, steel-concrete composite continuous beam bridges have been widely used in small- and medium-span bridges. In the negative moment zone of a continuous beam bridge, the concrete slab is under tension while the steel beam is under compression. During service, these beams are subjected to long-term random fatigue loads and environmental influences, making them prone to material deterioration problems such as concrete cracking and corrosion of the steel beams and reinforcing bars. The continuous accumulation of fatigue damage in the negative moment zone can eventually lead to fatigue failure of the structure or components, affecting the bridge's use and safety. To ensure the safe operation of bridges, it is necessary to predict fatigue failure in advance so that technical and management measures can be taken before fatigue failure occurs in the negative moment zone of the composite beam.

[0003] Stiffness degradation in the negative bending moment region of composite beams is an important indicator characterizing the bridge failure process. When calculating and predicting the stiffness degradation process in the negative bending moment region of steel-concrete composite beams, either time-domain or frequency-domain methods can be used. Analyzing the stiffness degradation law in the negative bending moment region of steel-concrete composite continuous beam bridges using the time-domain method requires sequential analysis of the random fatigue load loading process, resulting in a large computational workload. The frequency-domain method utilizes the overall distribution law of random fatigue loads for analysis, avoiding extensive calculations and efficiently obtaining the stiffness degradation law in the negative bending moment region of steel-concrete composite continuous beam bridges. Currently, there is no research on calculating and predicting the stiffness degradation process in the negative bending moment region of steel-concrete composite beams using the frequency-domain method. Summary of the Invention

[0004] The purpose of this invention is to provide a calculation method and storage medium for the stiffness degradation law of the negative bending moment zone of a steel-concrete composite beam under random fatigue loading based on fatigue cumulative damage theory and frequency domain method, so as to solve the technical problem of large calculation volume of time domain method for predicting the stiffness degradation process of the negative bending moment zone of steel-concrete composite beam in the prior art.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: to provide a method for calculating the stiffness degradation law in the negative bending moment zone of a steel-concrete composite beam, comprising the following steps: S100. Determine the random fatigue loads on the negative bending moment zone of the steel-concrete composite beam, including the peak and trough values ​​of each fatigue load, and calculate the amplitude of each fatigue load. S And the amplitude distribution law; the peak value, valley value and amplitude of fatigue load are all represented by the bending moment in the negative bending moment zone of the composite beam; S200. Perform curve fitting on the amplitude distribution of fatigue load to determine the probability density function of fatigue load amplitude. ; S300, Determine the fatigue life in the negative bending moment zone of the steel-concrete composite beam. ; S400, Determine the static load ultimate bearing moment of the negative bending moment zone of the steel-concrete composite beam. ; S500. Determine the stiffness reduction value of the steel-concrete composite beam at fatigue failure in the negative bending moment region. ; S600. Calculate the stiffness degradation law of steel-concrete composite beams under random fatigue load.

[0006] In one possible implementation, combining the above technical solutions, in S100, the random fatigue load is determined based on bridge health monitoring data.

[0007] In combination with the above technical solutions, one possible implementation method based on bridge health monitoring data is as follows: S110. Install strain gauges at the supports in the negative bending moment zone of the steel-concrete composite beam. The strain gauges are installed on the steel beam or concrete slab, and the installation position of the strain gauges is the strain acquisition point. S120. Use the installed strain gauges to collect strain time history data at the acquisition points during bridge operation, and construct a strain time history data curve. The strain time history data curve is a continuous curve with time on the horizontal axis and strain value on the vertical axis. Since the strain at the acquisition point will increase when a vehicle passes over the bridge, and the strain will return to the initial value after the vehicle passes, the strain time history data curve is a curve with a series of peaks and troughs. S130. Calculate the stress time history data at the acquisition point using strain time history data and the elastic modulus of steel or concrete. S140. Using stress time history data, and based on the relationship between the normal stress and the bending moment of the section in mechanics of materials, the bending moment time history data of the section is calculated. S150. The time history data of the bending moment on the section are processed by the rain flow counting method to obtain the amplitude distribution law of the bending moment. The bending moment amplitude is the difference between the peak value and the valley value of the bending moment for each fatigue load.

[0008] In one possible implementation, combining the above technical solutions, in S300, the fatigue life of the composite beam in the negative bending moment zone is characterized by fatigue fracture of the steel reinforcement within the concrete slab. The calculation formula is (1) In the formula, The bending moment amplitude in the negative bending moment zone of the composite beam is expressed in units of... , The moment of inertia of the composite beam section considering only the steel beam and reinforcing bars, in units of... , The vertical distance between the center of the uppermost longitudinal reinforcement and the centroid of the section when only considering the steel beam and the reinforcing bars are considered for the composite beam section is expressed in mm.

[0009] In one possible implementation, based on the above technical solutions, in S400, the static load ultimate bearing moment of the steel-concrete composite beam in the negative bending moment zone is... Determined through experiments.

[0010] In one possible implementation, based on the above technical solutions, in S400, the static load ultimate bearing moment of the steel-concrete composite beam in the negative bending moment zone is... Based on the principles of concrete structure design, the strength of the steel beam, the reinforcement ratio of the reinforced concrete slab, the strength of the steel bars, the strength of the concrete, and the cross-sectional dimensions of the components are calculated and determined.

[0011] In one possible implementation, based on the above technical solutions, the stiffness reduction value of the steel-concrete composite beam at fatigue failure in the negative bending moment region in S500 is... The calculation formula is: (2) In the formula, This refers to the bending moment amplitude borne by the composite beam in the negative bending moment zone. The static load ultimate bearing moment of the steel-concrete composite beam in the negative bending moment zone.

[0012] In one possible implementation, based on the above technical solutions, the stiffness degradation law of the steel-concrete composite beam in the negative bending moment region in S600 is expressed as follows: (3) In the formula, The stiffness of the steel-concrete composite beam after undergoing n random fatigue loads in the negative bending moment region. The initial stiffness of the steel-concrete composite beam in the negative bending moment region, where n is the number of random fatigue loads applied. The fatigue life of the composite beam in the negative bending moment region under random fatigue load is given. Let f be the probability density function of the fatigue load amplitude. This represents the decrease in stiffness of the composite beam during fatigue failure in the negative bending moment region.

[0013] To achieve the above objectives, the present invention provides a storage medium characterized in that it stores a computer program, which, when executed by a processor, implements the above-described method for calculating the stiffness degradation law in the negative bending moment zone of a steel-concrete composite beam.

[0014] The beneficial effects of the method and storage medium for calculating the stiffness of the negative bending moment zone of steel-concrete composite beams provided by this invention are as follows: Compared with the prior art, this invention can calculate and predict the stiffness degradation process of the negative bending moment zone of steel-concrete composite beams in advance, providing a theoretical basis for bridge maintenance and repair. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention, 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 The diagram shows the longitudinal reinforcement location of the steel-concrete composite beam in the calculation method for the stiffness degradation law in the negative bending moment zone of the steel-concrete composite beam provided in the embodiment of the present invention. In the diagram, OO is the location of the centroid of the section when only the steel beam and the reinforcement are considered.

[0017] Figure 2 A three-dimensional structural diagram of a steel-concrete composite beam for calculating the stiffness degradation law in the negative bending moment region of the steel-concrete composite beam provided in an embodiment of the present invention; Figure 3 A schematic diagram of the cross-sectional structure of a steel-concrete composite beam, which is used in the calculation method for the stiffness degradation law in the negative bending moment region of the steel-concrete composite beam provided in the embodiment of the present invention. Figure 4 A schematic diagram of the fatigue loading method for a steel-concrete composite beam, which is provided in the embodiment of the present invention for calculating the stiffness degradation law of the negative bending moment zone of the steel-concrete composite beam; Figure 5 The probability density function curve of the random fatigue bending moment amplitude in the negative bending moment region of the steel-concrete composite beam is provided in the calculation method of stiffness degradation law in the negative bending moment region of the steel-concrete composite beam provided in the embodiments of the present invention. Figure 6 The stiffness degradation curve in the calculation method of stiffness degradation law in the negative bending moment region of steel-concrete composite beam provided in the embodiments of the present invention; Figure 7 A comparison table of experimental and theoretical values ​​of the residual stiffness of the random fatigue test beam in the calculation method of stiffness degradation law in the negative bending moment zone of the steel-concrete composite beam provided in the embodiments of the present invention.

[0018] The labels for the attached figures are as follows: 10. Stud; 20. Movable support; 30. Concrete slab; 40. Steel beam; 50. Fixed support; 60. Reinforcing bar. Detailed Implementation

[0019] To make the technical problems, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the described embodiments are only a part of the embodiments of this application, not all of them. The specific embodiments described herein are only used to explain the invention and are not intended to limit the invention. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] The method for calculating the stiffness degradation law in the negative bending moment zone of steel-concrete composite beams and the storage medium provided by this invention are now described.

[0021] Stiffness degradation in the negative bending moment region of composite beams is a manifestation of accumulated fatigue damage. The accumulation of fatigue damage in the negative bending moment region of steel-concrete composite beams can be represented by stiffness degradation. The degradation law of composite beam stiffness is influenced by various factors, including external factors such as the number of loading cycles, the magnitude and distribution of fatigue loads, environmental factors, and construction quality, and internal factors such as structural bearing capacity, reinforcement ratio, material strength, and interface connection degree. The method for calculating the stiffness of steel-concrete composite beams in the negative bending moment region under random fatigue loading based on fatigue cumulative damage theory and frequency domain method provided in this invention fully considers the influence of these factors.

[0022] The following example illustrates the method for calculating the stiffness degradation law of a steel-concrete composite beam in the negative bending moment region provided by this invention. Specifically, MATLAB software is used to calculate the stiffness degradation law of a steel-concrete composite beam in the negative bending moment region under random fatigue load.

[0023] This steel-concrete composite beam is a single-span cantilever beam with a support spacing of 2.4m and a cantilever length of 1.4m. Random fatigue loads are applied to the cantilever ends, and the entire beam is in the negative bending moment region. A schematic diagram of the composite beam's three-dimensional structure and longitudinal dimensions is shown below. Figure 2 The beam cross-sectional shape and transverse dimensions are shown in [reference]. Figure 3 See loading method Figure 4 The steel-concrete composite beam uses C55 grade concrete, HRB400 grade steel bars with a diameter of 10mm for ordinary reinforcing bars, and Q345 steel for the steel beams.

[0024] S100. Determine the random fatigue loads on the negative bending moment zone of the steel-concrete composite beam, including the peak and trough values ​​of each fatigue load, and calculate the amplitude of each fatigue load. S The amplitude distribution pattern is also considered. The peak, trough, and amplitude of fatigue loads are all represented by the bending moment in the negative bending moment zone of the composite beam. Random fatigue loads can be determined based on bridge health monitoring data, as detailed below.

[0025] S110. Install strain gauges on the steel beam at the support of the negative bending moment zone of the steel-concrete composite beam. The strain gauges can be installed on the steel beam or the concrete slab. However, since the concrete in the negative bending moment zone is prone to cracking, the test data is inaccurate. Therefore, it is best to install the strain gauges on the steel beam. The installation position of the strain gauges is the strain acquisition point. S120. Use the installed strain gauges to collect strain time history data at the acquisition points during bridge operation, and construct a strain time history data curve. The strain time history data curve is a continuous curve with time on the horizontal axis and strain value on the vertical axis. Since the strain at the acquisition point will increase when a vehicle passes over the bridge, and the strain will return to the initial value after the vehicle passes over, the strain time history data curve is a curve with a series of peaks and troughs. S130. Calculate the stress time history data at the acquisition point using strain time history data and the elastic modulus of steel or concrete. S140. Using stress time history data, and based on the relationship between the normal stress and the bending moment of the section in mechanics of materials, the bending moment time history data of the section is calculated. S150. The time history data of the bending moment on the section are processed by the rain flow counting method to obtain the amplitude distribution law of the bending moment. The bending moment amplitude is the difference between the peak value and the valley value of the bending moment for each fatigue load.

[0026] S200. Perform curve fitting on the amplitude distribution of fatigue load to determine the probability density function of fatigue load amplitude. Curve fitting can be performed using MATLAB software based on the distribution law of bending moment amplitude obtained from S150. Following steps S110–S150 and S200, the random fatigue bending moment amplitude in the negative bending moment region of the steel-concrete composite beam follows a Gaussian distribution, and the probability density function curve of the bending moment amplitude is as follows: Figure 5 .

[0027] S300, Determine the fatigue life in the negative bending moment zone of the steel-concrete composite beam. The fatigue life of composite beams in the negative bending moment zone is characterized by fatigue fracture of the reinforcing steel in the concrete slab. The calculation formula is (1) In the formula, The bending moment amplitude in the negative bending moment zone of the composite beam is expressed in units of... , The moment of inertia of the composite beam section considering only the steel beam and reinforcing bars is expressed in units of . , refer to Figure 1 , The vertical distance between the center of the uppermost longitudinal reinforcement and the centroid of the section when only considering the steel beam and the reinforcing bars are considered for the composite beam section is expressed in mm.

[0028] S400. Determine the static load ultimate bearing moment of the negative bending moment zone of the steel-concrete composite beam. Measure the static load ultimate bearing moment of the composite beam in the negative bending moment zone using a static load test. .

[0029] The static load ultimate bearing moment of the negative bending moment zone of the steel-concrete composite beam Based on the principles of concrete structure design, the calculation is performed using the strength of the steel beam, the reinforcement ratio of the reinforced concrete slab, the strength of the reinforcing steel, the strength of the concrete, and the cross-sectional dimensions of the member. Since this calculation process is existing technology, it will not be detailed here. For specific calculation methods, please refer to the method provided in Chapter 3, Section 3, "Calculation of Bending Capacity of the Mid-Support Section," of *Design Principles of Steel-Concrete Composite Bridge Structures* (Second Edition) (ISBN 978-7-114-14390-8).

[0030] S500. Determine the stiffness reduction value of the steel-concrete composite beam at fatigue failure in the negative bending moment region. The decrease in stiffness of a steel-concrete composite beam at fatigue failure in the negative bending moment region. The calculation formula is: (2) In the formula, This refers to the bending moment amplitude borne by the composite beam in the negative bending moment zone. The static load ultimate bearing moment of the steel-concrete composite beam in the negative bending moment zone.

[0031] S600. Calculate the stiffness degradation law of steel-concrete composite beam in the negative bending moment zone under random fatigue load.

[0032] According to Miner's linear damage accumulation theory, the damage caused by fatigue loading is independent of the loading sequence. The damage caused by constant amplitude fatigue loading can be represented by the residual stiffness model as follows: (4) In equation (4), This represents the fatigue damage value in the negative bending moment zone of the composite beam. Indicates constant amplitude fatigue load loading Stiffness of the negative bending moment region of the secondary composite beam This represents the initial stiffness of the composite beam in the negative bending moment region. This indicates fatigue failure in the negative bending moment zone of the composite beam (i.e., the number of loading cycles equals the fatigue life). Stiffness at that time The number of times a constant amplitude fatigue load is applied. This represents the fatigue life in the negative bending moment zone of the composite beam.

[0033] Normalizing equation (4) yields (5) Under random fatigue loading, the random fatigue load is considered as a multi-stage constant amplitude fatigue load. For any level of constant amplitude fatigue load Equation (5) holds true, that is (6) In equation (6), For the i-th level constant amplitude fatigue load Loading count, For the i-th level constant amplitude fatigue load Fatigue life of composite beam in negative bending moment region under load. Indicates constant amplitude fatigue load load Stiffness of the negative bending moment region of the secondary composite beam Represents the i-th level constant amplitude fatigue load Stiffness of the composite beam under negative bending moment region during fatigue failure.

[0034] Taking the differential of both sides of equation (6), we get (7) The residual stiffness increment of the composite beam in the negative moment region under random fatigue loading is: (8) For continuously distributed stress states, drawing on frequency domain stochastic lifetime estimation methods, for a given stationary stochastic load process, the load range ( , The number of load cycles within ) is (9) In equation (9), n represents the number of random fatigue load applications. Fatigue load increment.

[0035] Taking the differential of both sides of equation (9), we get (10) Substituting equation (10) into equation (8), we get (11) For continuous stress states, equation (11) can be written in integral form as follows: (12) Integrating equation (12) yields (13) make , This represents the decrease in stiffness at fatigue failure in the negative bending moment zone of a steel-concrete composite beam.

[0036] By fitting multiple experimental data, we obtain (14) In equation (14), S This refers to the bending moment amplitude experienced by the composite beam in the negative bending moment region. The static load ultimate bearing moment of the negative bending moment zone of the composite beam is given by equation (13), which can be written as follows: (3) In the formula, The stiffness of the steel-concrete composite beam after undergoing n random fatigue loads in the negative bending moment region. The initial stiffness of the steel-concrete composite beam in the negative bending moment region, where n is the number of random fatigue loads applied. The fatigue life of the composite beam in the negative bending moment region under random fatigue load is given. Let f be the probability density function of the fatigue load amplitude. This represents the decrease in stiffness of the composite beam during fatigue failure in the negative bending moment region.

[0037] Figure 6 This is the stiffness degradation curve of the composite beam in the negative bending moment region, calculated based on an example. (Example:) Figure 7 As shown, by comparing with the experimental values, it can be seen that the maximum difference between the calculation results of the steel-concrete composite beam stiffness degradation calculation method based on fatigue cumulative damage theory and frequency domain method proposed in this invention and the experimental values ​​is -8.385%. The two are in good agreement, indicating that the method can obtain relatively reasonable results in predicting the stiffness degradation law of steel-concrete composite beams in the negative bending moment region.

[0038] The method for calculating stiffness degradation in the negative bending moment zone of steel-concrete composite beams proposed in this invention can calculate and predict the stiffness degradation process in the negative bending moment zone of steel-concrete composite beams in advance, providing a theoretical basis for bridge maintenance and repair.

[0039] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the stiffness degradation law in the negative bending moment region of a steel-concrete composite beam, characterized in that, Includes the following steps: S100. Determine the random fatigue loads on the negative bending moment zone of the steel-concrete composite beam, including the peak and trough values ​​of each fatigue load, and calculate the amplitude of each fatigue load. S The amplitude distribution law; the peak value, valley value and amplitude of fatigue load are all represented by the bending moment at the support of the negative bending moment zone of the composite beam; S200. Perform curve fitting on the amplitude distribution of fatigue load to determine the probability density function of fatigue load amplitude. ; S300, Determine the fatigue life in the negative bending moment zone of the steel-concrete composite beam. ; S400, Determine the static load ultimate bearing moment of the negative bending moment zone of the steel-concrete composite beam. ; S500. Determine the stiffness reduction value of the steel-concrete composite beam at fatigue failure in the negative bending moment region. ; S600. Calculate the stiffness degradation law of steel-concrete composite beams under random fatigue load.

2. The method for calculating the stiffness degradation law in the negative bending moment region of steel-concrete composite beams as described in claim 1, characterized in that: In S100, random fatigue loads are determined based on bridge health monitoring data.

3. The method for calculating the stiffness degradation law in the negative bending moment region of steel-concrete composite beams as described in claim 2, characterized in that, The method used to determine this based on bridge health monitoring data is as follows: S110. Install strain gauges at the supports in the negative bending moment zone of the steel-concrete composite beam. The strain gauges are installed on the steel beam or concrete slab, and the installation position of the strain gauges is the strain acquisition point. S120. Use the installed strain gauges to collect strain time history data at the acquisition points during bridge operation, and construct a strain time history data curve. The strain time history data curve is a continuous curve with time on the horizontal axis and strain value on the vertical axis. Since the strain at the acquisition point will increase when a vehicle passes over the bridge, and the strain will return to the initial value after the vehicle passes over, the strain time history data curve is a curve with a series of peaks and troughs. S130. Calculate the stress time history data at the acquisition point using strain time history data and the elastic modulus of steel or concrete. S140. Using stress time history data, and based on the relationship between the normal stress and the bending moment of the section in mechanics of materials, the bending moment time history data of the section is calculated. S150. The time history data of the bending moment on the section are processed by the rain flow counting method to obtain the amplitude distribution law of the bending moment. The bending moment amplitude is the difference between the peak value and the valley value of the bending moment for each fatigue load.

4. The method for calculating the stiffness degradation law in the negative bending moment region of steel-concrete composite beams as described in claim 1, characterized in that: In S300, the fatigue life of composite beams in the negative bending moment zone is characterized by fatigue fracture of the steel reinforcement within the concrete slab. The calculation formula is （1） In the formula, This represents the bending moment amplitude in the negative bending moment zone of the composite beam. For composite beam sections, considering only the moment of inertia of the steel beam and reinforcing bars, For composite beam sections, considering only the steel beam and reinforcing bars, the vertical distance between the center of the uppermost longitudinal reinforcing bar and the centroid of the section is considered.

5. The method for calculating the stiffness degradation law in the negative bending moment region of steel-concrete composite beams as described in claim 1, characterized in that: In S400, the static load ultimate bearing moment of the steel-concrete composite beam in the negative bending moment zone. Determined through experiments.

6. The method for calculating the stiffness degradation law in the negative bending moment region of steel-concrete composite beams as described in claim 1, characterized in that: In S400, the static load ultimate bearing moment of the steel-concrete composite beam in the negative bending moment zone. Based on the principles of concrete structure design, the strength of the steel beam, the reinforcement ratio of the reinforced concrete slab, the strength of the steel bars, the strength of the concrete, and the cross-sectional dimensions of the component are used for calculation.

7. The method for calculating the stiffness degradation law in the negative bending moment region of steel-concrete composite beams as described in claim 1, characterized in that: In S500, the decrease in stiffness at fatigue failure in the negative bending moment region of a steel-concrete composite beam. The calculation formula is: （2） In the formula, This refers to the bending moment amplitude borne by the composite beam in the negative bending moment zone. The static load ultimate bearing moment of the steel-concrete composite beam in the negative bending moment zone.

8. The method for calculating the stiffness degradation law in the negative bending moment region of steel-concrete composite beams as described in claim 1, characterized in that: In S600, the stiffness degradation law of the negative bending moment region of steel-concrete composite beams is expressed as follows: （3） In the formula, The stiffness of the steel-concrete composite beam after undergoing n random fatigue loads in the negative bending moment region. Let be the initial stiffness of the steel-concrete composite beam in the negative bending moment region, and n be the number of random fatigue loads applied. The fatigue life of the composite beam in the negative bending moment region under random fatigue load is given. Let f be the probability density function of the fatigue load amplitude. This represents the decrease in stiffness of the composite beam during fatigue failure in the negative bending moment region.

9. A storage medium, characterized in that, It stores a computer program, which, when executed by a processor, implements the calculation method for the stiffness degradation law in the negative bending moment zone of the steel-concrete composite beam as described in any one of claims 1-8.

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