Concrete box girder nonlinear damage identification method considering shear hysteresis effect
By arranging long gauge-length strain sensors in the concrete box girder, the neutral axis height and bending stiffness were determined, solving the problem of the unconsidered shear lag effect. This enabled sensitive identification of local damage and full-process damage assessment, improving the identification accuracy and assessment precision.
Patent Information
- Application Number
- CN202511927137.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-19
- Publication Date
- 2026-03-20
AI Technical Summary
Existing technologies fail to effectively consider shear lag effects in damage identification of concrete box girders, and damage identification methods based on macroscopic response are not sensitive to local damage, making it difficult to accurately assess the service performance and durability of the structure.
A nonlinear damage identification method considering shear hysteresis effect is adopted. By arranging long gauge-length strain sensors, the neutral axis height and bending stiffness are determined. The curvature distribution is obtained by long gauge-length strain inversion, and the equivalent bending stiffness is calculated to reflect local stiffness changes and quantify the degree of damage.
It enables nonlinear damage identification of concrete box girders, accurately reflects local damage and global response, improves identification accuracy, is applicable to the entire process of structural failure, and provides quantitative damage assessment.
Smart Images
Figure CN121705653A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for identifying damage in concrete box girders, specifically a nonlinear damage identification method for concrete box girders that considers shear lag effects. Background Technology
[0002] Concrete box girders, as a structural form with high cross-sectional stiffness and convenient construction, have been widely used in modern beam bridge engineering. Compared with rectangular beams, concrete box girders have higher torsional stiffness and overall stability due to their closed thin-walled cross-section; the hollow structure reduces self-weight while ensuring load-bearing capacity, and also has the characteristics of convenient construction and excellent durability. Therefore, they have become an efficient and economical structural form in modern bridge engineering.
[0003] In concrete box girder structures, damage gradually accumulates due to the combined effects of structural material aging, external environmental corrosion, long-term load effects, fatigue effects, and accidental loads (such as surcharges). The coupled effects of these factors lead to more complex mechanical and durability issues for concrete box girders during long-term service. Due to factors such as shear hysteresis, the nonlinear behavior of concrete box girders is significant, resulting in complex failure modes under extreme loads. Therefore, accurately assessing the service performance, safety performance, and durability of concrete box girders has become a core research topic. Finite element model correction is a commonly used method for identifying structural parameters. These parameters can be obtained by modifying physical parameters within the finite element model, minimizing the difference between the finite element model calculation and the calculated response.
[0004] Currently, there are many finite element model correction methods based on different objective functions: first, methods based on dynamic modal parameters; second, methods based on static response; and third, methods based on both dynamic and static responses. Although these finite element model correction methods have been successfully applied to the estimation of structural parameters, they still have shortcomings: they do not consider the shear lag effect in box girder structures, and current damage identification methods based on macroscopic responses (displacement, frequency, etc.) are not sensitive to local damage. Summary of the Invention
[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a nonlinear damage identification method for concrete box girders that considers shear lag effects. This method does not require a finite element model and can take into account nonlinearity and shear lag effects. Furthermore, this method is applicable to the entire process of structural failure.
[0006] The technical solution adopted in this invention is: a nonlinear damage identification method for concrete box girders considering shear lag effect, comprising the following steps: Step 1: Determining the neutral axis height of the concrete box girder: Step 1: Putm A long gauge-length strain gauge is arranged at the bottom of the concrete box girder. j The coverage area is represented as a cell. j The concrete box girder satisfies the plane section assumption. Step 2: Divide the concrete box girder into several equal-thickness strips along the height direction. According to the static equilibrium condition, the resultant tensile and compressive axial forces of the concrete and steel bars in the section are equal. An approximate value of the neutral axis height is obtained through statistical methods. Step 3: To ensure that the neutral axis height meets the equilibrium condition, establish an error function. To reflect the deviation of the centering shaft height; when If the value is infinitely close to or equal to 0, it indicates that under the assumed neutral axis height calculation, the resultant force in the tension and compression zone of the section is in equilibrium, and the iterated neutral axis height is the true neutral axis height. Step 2: Steps for identifying bending stiffness: Step 1: After determining the actual neutral shaft height, calculate the unit. j The pure bending curvature; Step 2: Based on the linear relationship between deflection distribution and curvature distribution, considering the shear lag effect of concrete box girder, the shear lag corrected deflection of concrete box girder is obtained. Step 3: Calculate the flexural stiffness of the concrete box girder based on the corrected curvature; Step 4: The relative degradation of beam element stiffness is represented by the flexural stiffness of the beam section in the intact state and the average flexural stiffness of the section after cracking, thus serving as a quantitative indicator of the degree of damage.
[0007] Furthermore, in step 1 of step one: the span, height, and width of the concrete box girder are respectively represented by... L , h and b Representation; Unit j In the above, let the sensor gauge length be... The strain measured by the sensor is ; Average strain measured by long gauge length sensor Discretization modeling is performed, and then further converted into cross-sectional curvature values. ; The cross section still satisfies the plane section assumption after deformation, meaning the original cross section remains straight after deformation, with only rotation of the neutral axis occurring; the height of the neutral axis from the bottom surface of the beam is... Then any height within the cross section y The strain distribution at the location is as follows: (1).
[0008] Furthermore, in step 2 of step one: the average bending moment of beam element j under external load. Represented as: (2) In the formula, To calculate the tensile stress in the concrete at the location; The reinforcement is assumed to be under tensile stress at the neutral axis height; This represents the cross-sectional area of the tension reinforcement. To calculate the compressive stress of the concrete at the location; The stress on the reinforcing steel at the assumed neutral axis height; This represents the cross-sectional area of the compressed reinforcing steel. The distance between the center of the tensioned reinforcement and the neutral axis; The distance between the center of the compressed steel bar and the neutral axis; The resultant tensile and compressive axial forces of the concrete and reinforcing steel in the cross-section must satisfy the equilibrium condition: (3) When the assumed neutral axis height satisfies formula (3), it indicates that the internal forces of the section are in equilibrium. Therefore, the assumed neutral axis height is the actual neutral axis height. Calculating the internal force equilibrium of the section by assuming the neutral axis height is a process of obtaining the optimal solution through iterative solution. An approximate value of the neutral axis height is obtained through statistical methods.
[0009] Furthermore, in step 3 of step one: an error function is established to reflect the deviation of the assumed neutral axis height, and the error function of the total resultant force is expressed as: (4) In the formula, These are the resultant forces in the tensile and compressive zones of the concrete section, respectively, obtained by integrating the stress-strain relationship of the concrete. These are the resultant forces in the tension and compression zones of the reinforcing bars, respectively, which are calculated by summing the area of the reinforcing bars and the corresponding stresses. When the error function is infinitely close to or equal to 0 in value, it indicates that the assumed neutral axis height is the true neutral axis height.
[0010] Furthermore, in step 1 of step two: determining the actual center and shaft height... At that time, unit j The pure bending curvature is as follows (5).
[0011] Furthermore, in step 2 of step two: the corrected deflection caused by the shear lag is calculated. (6).
[0012] Furthermore, in step 3 of step two: the shear hysteresis is converted into an "equivalent curvature" contribution. (7) Therefore, the corrected curvature of the beam, after considering the shear lag effect, is: (8) The equivalent bending stiffness is obtained by dividing the bending moment by the corrected curvature: (9).
[0013] Furthermore, in step 4 of step two: after the beam-type concrete structure is damaged and cracked, the neutral axis of the cross section will rise, and the bending stiffness of the structure will decrease. The change in local bending stiffness can reflect the generation of random cracks and the entire process of structural damage and degradation under increased external load, and therefore serves as a quantitative indicator of the degree of damage; the bending stiffness of the beam element cross section is constant when the structure is intact. The average flexural stiffness of the interface after damage and cracking of the beam element is The relative degradation of beam element stiffness is expressed as: (10).
[0014] This invention proposes a nonlinear damage identification method for box girders (using long gauge length strain response to determine the bending stiffness before and after damage, thereby obtaining the relative degree of stiffness degradation). Theoretical derivation shows that the neutral axis position of the box girder can be estimated by long gauge length strain and material properties, and then the curvature distribution, bending stiffness, and deflection can be determined. Simulation results show that the evaluation parameter (bending stiffness) can clearly and quantitatively reflect the degradation process of the box girder. Furthermore, long gauge length strain can reflect both the global response and capture local changes, and the structural response obtained by its inversion is highly consistent with the measured results. Compared with finite element model correction methods, this method does not require a finite element model and can consider nonlinear and shear lag effects. Moreover, this method is applicable to the entire process of structural failure.
[0015] The beneficial effects of this invention are: (1) Compared with traditional point strain sensors, long-range strain sensors can cover damage, so parameter estimation can take into account the nonlinearity of the structure.
[0016] (2) Traditional macroscopic response methods are not sensitive to local damage, while this method directly utilizes the neutral axis height and curvature distribution obtained by long gauge length strain inversion. Since these mechanical quantities are highly sensitive to local stiffness attenuation, they can effectively identify the occurrence and development of local cracks or local damage.
[0017] (3) This method uses local strain data to calculate the equivalent bending stiffness, which can reflect the local stiffness changes of each unit section of the beam, thereby quantitatively describing the spatial distribution of structural damage.
[0018] (4) By calculating the degree of local stiffness degradation at different loading stages, the evolution process of crack development and structural damage can be displayed intuitively, which not only reflects the existence of damage, but also reveals the trend of damage development.
[0019] (5) This method takes into account the shear lag effect of box girders, which further improves the identification accuracy and is applicable to various box-type concrete beams. Attached Figure Description
[0020] Figure 1 This is the strain distribution of the beam in this invention.
[0021] Figure 2 This describes the stress state and strain distribution of the box girder section of the present invention.
[0022] Figure 3 a represents the constitutive model of the material in this invention (tensile concrete).
[0023] Figure 3 b is the constitutive model of the material of this invention (compressed concrete).
[0024] Figure 4 This invention provides a process for identifying nonlinear damage in box girders.
[0025] Figure 5 This is the load-strain curve of the present invention.
[0026] Figure 6 This is the equivalent bending stiffness of the present invention.
[0027] Figure 7 This represents the relative degradation degree of the box girder unit in this invention. Detailed Implementation
[0028] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.
[0029] like Figure 4 As shown, a nonlinear damage identification method for concrete box girders considering shear lag effects includes the following steps: (a) Method for determining the neutral axis height of a box girder Assuming a total of m Several long gauge-length strain sensors (measuring the average strain of the unit) are distributed at the bottom of the box girder. The span, height, and width of the box girder are respectively represented by... L , h and b Indicated by the sensor. j The coverage area is represented as a cell. j . By unit j For example, let the sensor gauge length be... The strain measured by the sensor is .
[0030] Average strain measured by long gauge length sensor Press Figure 1 The model is discretized as shown and further converted into cross-sectional curvature values. .
[0031] It is reasonable to assume that the cross section still satisfies the plane section assumption after deformation, that is, the original cross section remains flat after deformation, and only the neutral axis rotates. For example... Figure 2 The height from the neutral axis to the bottom surface of the beam is Then any height within the cross section y The strain distribution at the location is as follows: (1) For tensile concrete, Hordijk proposed a constitutive model that reflects crack softening ( Figure 3 a) Young's modulus :tensile strength, Cracking strain; the relationship model of concrete under compression is as follows: Figure 3 As shown in b. Compressive strength For reinforcement, an ideal elastoplastic constitutive model is used.
[0032] Average bending moment of beam element j under external load It can be represented as: (2) In the formula, To calculate the tensile stress in the concrete at the location; The reinforcement is assumed to be under tensile stress at the neutral axis height; This represents the cross-sectional area of the tension reinforcement. To calculate the compressive stress of the concrete at the location; The stress on the reinforcing steel at the assumed neutral axis height; This represents the cross-sectional area of the compressed reinforcing steel. The distance between the center of the tensioned reinforcement and the neutral axis; It is the distance between the center of the compressed steel bar and the neutral axis.
[0033] Actual reinforced concrete box girder sections exhibit significant nonlinear material response characteristics after loading. Therefore, the position of the neutral axis in the section cannot be directly obtained from linear elastic theory and must be determined through static equilibrium conditions. Specifically, the resultant tensile and compressive axial forces of the concrete and reinforcing steel in the section must satisfy the following equilibrium conditions: (3) When the assumed neutral axis height satisfies formula (3), it indicates that the internal forces of the cross section are in equilibrium. Therefore, the assumed neutral axis height is the actual neutral axis height. Calculating the internal force equilibrium of the cross section by assuming the neutral axis height is a process of obtaining the optimal solution through iterative solution. An approximate value of the neutral axis height can be obtained through statistical methods, and an error function can be established to reflect the deviation of the assumed neutral axis height. The error function of the total resultant force can be expressed as: (4) In the formula, These are the resultant forces in the tensile and compressive zones of the concrete section, respectively, obtained by integrating the stress-strain relationship of the concrete. These are the resultant forces in the tension and compression zones of the reinforcing bars, respectively, which are calculated by summing the area of the reinforcing bars and the corresponding stresses.
[0034] When the error function is infinitely close to or equal to 0 in value, it indicates that the assumed neutral axis height is the true neutral axis height.
[0035] (II) Methods for Identifying Bending Stiffness The above method solves the problem of determining the neutral axis height of the box girder. Next, we will identify the bending stiffness of the box girder.
[0036] Determining the actual shaft height At that time, unit j The pure bending curvature is as follows (5) According to the Reissner-Vlasov shear lag theory, we can calculate the additional deflection caused by shear lag: (6) Transforming shear hysteresis into an "equivalent curvature" contribution: (7) Therefore, the corrected curvature of the beam, after considering the shear lag effect, is: (8) The equivalent bending stiffness is obtained by dividing the bending moment by the corrected curvature: (9) After damage and cracking occur in a beam-type concrete structure, the neutral axis of the cross-section will rise, and the flexural stiffness of the structure will decrease. Changes in local flexural stiffness can reflect the entire process of random crack formation and structural damage degradation under increased external loads, and therefore can serve as a quantitative indicator of the degree of damage. In a structurally intact state, the flexural stiffness of a beam element is constant. The average flexural stiffness of the interface after damage and cracking of the beam element is The relative degradation of the stiffness of a beam element can be expressed as: (10).
[0037] The box girder model was simulated and verified using the above method. The test beam was a single-cell reinforced concrete box girder with a clear span of 2960 mm, and was subjected to a four-point bending load. The total height of the beam section was 280 mm, the top plate thickness was 30 mm, the bottom plate thickness was 45 mm, the web thickness was 62 mm, and the center distance between the two webs was 475 mm; the total width of the outer edge of the top plate of the box girder was 1000 mm. Strain sensors were placed in regions S1 to S3 of the beam to obtain local strain information at different cross-sectional locations. Since the beam geometry, loading method, and sensor arrangement are symmetrical, theoretically the strains in S1 and S3 should be completely identical. However, the experimental results showed that there were certain differences between them, such as... Figure 5 This is mainly due to the non-uniformity of concrete materials and the random development of local cracks, which results in differences in local stiffness in different cross-sectional areas.
[0038] Based on the local strain data from each sensor, the corresponding equivalent bending stiffness can be calculated, such as... Figure 6 As shown, the equivalent bending stiffness reflects the bending capacity of each beam element under external loads, revealing the spatial distribution of the beam section's load-bearing capacity and its local stiffness differences. By comparing the equivalent bending stiffness at different loading stages, a trend can be observed where the structural stiffness gradually decreases with increasing load; this change is closely related to crack propagation and local damage accumulation.
[0039] By further utilizing the local stiffness degradation index defined by formula (10), the relative stiffness degradation degree of each beam element can be calculated, such as... Figure 7 As shown, the relative degradation degree can quantitatively reflect the decrease in local stiffness of the beam section, and can effectively describe the development and accumulation of damage in the structure during loading. The analysis of local equivalent bending stiffness and its degradation index can not only reveal the spatial distribution law of structural damage, but also provide a reliable quantitative basis for subsequent structural health monitoring and safety assessment.
[0040] The detailed description of the above embodiments is not intended to limit the scope of protection claimed by the present invention, but merely to illustrate selected embodiments of the invention. For those skilled in the art, various changes, modifications, substitutions, and variations of these embodiments within the scope of the principles and technical ideas of the present invention will still fall within the protection scope of the present invention.
Claims
1. A nonlinear damage identification method for concrete box girders considering shear lag effect, characterized in that: Includes the following steps: Step 1: Determining the neutral axis height of the concrete box girder: Step 1: Put m A long gauge-length strain gauge is arranged at the bottom of the concrete box girder. j The coverage area is represented as a cell. j The concrete box girder satisfies the plane section assumption. Step 2: Divide the concrete box girder into several equal-thickness strips along the height direction. According to the static equilibrium condition, the resultant tensile and compressive axial forces of the concrete and steel bars in the section are equal. An approximate value of the neutral axis height is obtained through statistical methods. Step 3: To ensure that the neutral axis height meets the equilibrium condition, establish an error function. To reflect the deviation of the centering shaft height; when If the value is infinitely close to or equal to 0, it indicates that under the assumed neutral axis height calculation, the resultant force in the tension and compression zone of the section is in equilibrium, and the iterated neutral axis height is the true neutral axis height. Step 2: Steps for identifying bending stiffness: Step 1: After determining the actual neutral shaft height, calculate the unit. j The pure bending curvature; Step 2: Based on the linear relationship between deflection distribution and curvature distribution, considering the shear lag effect of concrete box girder, the shear lag corrected deflection of concrete box girder is obtained. Step 3: Calculate the flexural stiffness of the concrete box girder based on the corrected curvature; Step 4: The relative degradation of beam element stiffness is represented by the flexural stiffness of the beam section in the intact state and the average flexural stiffness of the section after cracking, thus serving as a quantitative indicator of the degree of damage.
2. The nonlinear damage identification method for concrete box girders considering shear lag effect according to claim 1, characterized in that: In step 1 of step one: the span, height, and width of the concrete box girder are respectively represented by... L , h and b Representation; Unit j In the above, let the sensor gauge length be... The strain measured by the sensor is ; Average strain measured by long gauge length sensor Discretization modeling is performed, and then further converted into cross-sectional curvature values. ; The cross section still satisfies the plane section assumption after deformation, meaning the original cross section remains straight after deformation, with only rotation of the neutral axis occurring; the height of the neutral axis from the bottom surface of the beam is... Then any height within the cross section y The strain distribution at the location is as follows: （1）。 3. The nonlinear damage identification method for concrete box girders considering shear lag effect according to claim 2, characterized in that: In step 2 of step one: the average bending moment of beam element j under external load. Represented as: （2） In the formula, To calculate the tensile stress in the concrete at the location; The reinforcement is assumed to be under tensile stress at the neutral axis height; This represents the cross-sectional area of the tensile reinforcement. To calculate the compressive stress of the concrete at the location; The stress on the reinforcing steel at the assumed neutral axis height; This represents the cross-sectional area of the compressed reinforcing steel. The distance between the center of the tensioned reinforcement and the neutral axis; The distance between the center of the compressed steel bar and the neutral axis; The resultant tensile and compressive axial forces of the concrete and reinforcing steel in the cross-section must satisfy the equilibrium condition: （3） When the assumed neutral axis height satisfies formula (3), it indicates that the internal forces of the section are in equilibrium. Therefore, the assumed neutral axis height is the actual neutral axis height. Calculating the internal force equilibrium of the section by assuming the neutral axis height is a process of obtaining the optimal solution through iterative solution. An approximate value of the neutral axis height is obtained through statistical methods.
4. The nonlinear damage identification method for concrete box girders considering shear lag effect according to claim 3, characterized in that: In step 3 of step one: an error function is established to reflect the deviation of the assumed neutral axis height. The error function of the total resultant force is expressed as follows: （4） In the formula, These are the resultant forces in the tensile and compressive zones of the concrete section, respectively, obtained by integrating the stress-strain relationship of the concrete. These are the resultant forces in the tension and compression zones of the reinforcing bars, respectively, which are calculated by summing the area of the reinforcing bars and the corresponding stresses. When the error function is infinitely close to or equal to 0 in value, it indicates that the assumed neutral axis height is the true neutral axis height.
5. The nonlinear damage identification method for concrete box girders considering shear lag effect according to claim 4, characterized in that: In step 1 of step two: determining the actual neutral shaft height. At that time, unit j The pure bending curvature is as follows （5）。 6. The nonlinear damage identification method for concrete box girders considering shear lag effect according to claim 5, characterized in that: In step 2 of step two: the corrected deflection caused by the shear hysteresis is calculated. （6）。 7. The nonlinear damage identification method for concrete box girders considering shear lag effect according to claim 6, characterized in that: In step 3 of step two: the shear hysteresis is converted into an "equivalent curvature" contribution. （7） Therefore, the corrected curvature of the beam, after considering the shear lag effect, is: （8） The equivalent bending stiffness is obtained by dividing the bending moment by the corrected curvature: （9）。 8. The nonlinear damage identification method for concrete box girders considering shear lag effect according to claim 7, characterized in that: In step 4 of step two: after damage and cracking of the beam-type concrete structure, the neutral axis of the cross section will rise, and the bending stiffness of the structure will decrease. The change in local bending stiffness can reflect the generation of random cracks and the entire process of structural damage and degradation under increased external load, and therefore serves as a quantitative indicator of the degree of damage; the bending stiffness of the beam element cross section is constant when the structure is intact. The average flexural stiffness of the interface after damage and cracking of the beam element is... The relative degradation of beam element stiffness is expressed as: （10）。