Beam body bearing capacity evaluation method based on rigidity distribution identification

Abstract

The invention discloses a beam body bearing capacity assessment method based on rigidity distribution identification, and relates to the technical field of civil or bridge structure health monitoring. The method comprises the following steps: firstly, carrying out geometric segmentation on a to-be-evaluated beam body, applying a static load, measuring node deflection and selectively measuring a rotation angle; and constructing a total stiffness matrix by taking the flexural stiffness of each section as an unknown number, constructing an equilibrium equation in combination with boundary conditions and loads, and solving to obtain the distribution condition of the flexural stiffness along the beam length and the flexural stiffness of the minimum beam section. Secondly, by analyzing the consistency of rigidity distribution under different loading grades and comparing with historical data, the linear elasticity condition and damage development of the beam body are judged. And finally, establishing a rigidity and bearing capacity parameter relationship based on the material and section data, and reversely deducing the weakest section bearing capacity and the maximum bearing capacity of the beam body by utilizing the minimum rigidity. The method can accurately position the rigidity weakening area and quantitatively reflect the damage, the identification result is accurate, the operation is simple and convenient, and the cost is low.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of civil or bridge structure health monitoring, and particularly relates to a beam bearing capacity evaluation method based on stiffness distribution identification. BACKGROUND

[0002] With the rapid development of China's transportation infrastructure, a large number of existing bridges gradually enter the post-service period. Influenced by multiple factors such as material aging, environmental erosion, traffic load growth, design standard improvement, etc., the actual bearing capacity of some bridges may be lower than the current use demand, and there is a certain structural safety hazard. Therefore, accurately evaluating the bearing capacity of existing bridges has important engineering value and social significance for ensuring the safe operation of bridges and guiding scientific maintenance and reinforcement decisions.

[0003] At present, the evaluation methods for the bearing capacity of beam structures in engineering practice mainly include the equivalent bending stiffness calculated based on the simplified deflection formula, the stiffness identification based on modal parameters (frequency and mode shape), and the inversion method based on finite element model parameter correction. Although these methods have certain application basis, they generally have problems such as difficulty in accurately obtaining the distribution of stiffness along the beam length, sensitivity to external environment, boundary and loading conditions, high requirement for measurement point arrangement, lack of unified mechanism for solving over-determined / under-determined problems, etc., resulting in unstable and insufficient accuracy of the identification results. In addition, the existing methods lack the reverse mechanism from the stiffness parameter to the key indicators of bearing capacity (such as cross-sectional height, steel area, etc.), and the mutual relationship and influence mechanism of stiffness and bearing capacity are not clear, which often can only perform qualitative evaluation of bearing capacity, and it is difficult to meet the engineering requirements.

[0004] At present, there is a need for a beam evaluation method that can accurately identify the distribution of stiffness along the beam length and give accurate quantitative results of bearing capacity based on the distribution of stiffness, in order to improve the accuracy, adaptability and engineering practicability of the evaluation. SUMMARY

[0005] In view of the deficiencies of the existing beam bearing capacity evaluation methods, the present application provides a beam bearing capacity evaluation method based on stiffness distribution identification. In the static load working condition of the beam, the distribution of stiffness along the beam length is obtained by arranging limited displacement or angle measurement points. According to the theoretical relationship between the stiffness, load effect and deformation of the beam under load, the key parameters affecting the bearing capacity (such as effective cross-sectional height, steel area, etc.) are obtained, and then the bearing capacity of the beam is evaluated by combining the minimum stiffness principle. According to the displacement or angle information of the beam under load, the present application obtains the stiffness distribution of the beam, and through the analysis of the stiffness distribution, the local stiffness weakening area of the beam can be accurately located, and the damage degree can be quantitatively reflected. Furthermore, the identification results can be converted into bearing capacity indicators, which has the advantages of accurate identification results, simple operation and low cost.

[0006] The application achieves the technical solutions below.

[0007] A beam body bearing capacity evaluation method based on stiffness distribution identification, comprising the following steps:

[0008] S1, the geometry of the beam body to be evaluated is segmented, static load is applied to the nodes step by step, the load size is recorded, the deflection information of the nodes between the segments is measured, and the rotation angle information of the nodes is selectively measured;

[0009] S2, the bending stiffness EI(n) of each segment of the segmented beam body is taken as an unknown quantity, and the overall stiffness matrix K of the beam body is constructed;

[0010] S3, the balance equation KU=F is constructed in combination with the boundary conditions of the beam body, the deformation matrix U and the load matrix F;

[0011] S4, the balance equation is solved to obtain the distribution of the bending stiffness EI(n) of each segment of the beam body along the beam length, that is, the bending stiffness distribution, and the minimum beam segment bending stiffness EI min is identified;

[0012] S5, the bending stiffness distribution of the beam body under different loading levels is compared to determine the linear elasticity of the beam body; if the bending stiffness of each segment under different loading levels is consistent, it is determined that the linear elasticity of the beam body is good, otherwise it is determined that there is serious damage;

[0013] S6, on the basis of good linear elasticity of the beam body, the bending stiffness distribution under the last level of loading is compared with the historical bending stiffness distribution to determine whether there is new damage and the development of the damage;

[0014] S7, the relationship between the bending stiffness and the key parameters of the bearing capacity is derived according to the material and cross-sectional size data of the beam body, the bearing capacity M max of the thinnest section is calculated according to the minimum beam segment bending stiffness EI min , and the maximum bearing capacity F max is solved in combination with the boundary conditions and the loading conditions.

[0015] Further, S1 specifically includes the following sub-steps:

[0016] S101, displacement sensors are arranged on the nodes, and the displacement sensors collect data by using a wire displacement gauge, a top rod displacement gauge, a laser displacement gauge or a vision-based displacement measurement method;

[0017] S102, loads are applied to part of the nodes, a step loading method is used, the last level of applied load does not exceed the load under normal working conditions of the beam body, and the deflection data of the nodes and the selectively measured rotation angle data are recorded synchronously during the loading process;

[0018] Further, S2 specifically comprises the following sub-steps:

[0019] S201, dividing the beam body with a beam length of L into n beam segments, each with a length of l, and the corresponding bending stiffness being EI(n), the vertical displacement and rotation angle of the node being v1, v2, v 3… v n+1 and θ1, θ2, θ 3… θ n+1 ; establishing the element stiffness matrix K n of the nth beam segment, and its expression is as follows:

[0020] ; wherein i, j are the left and right nodes of the beam segment;

[0021] S202, assembling the element stiffness matrix K n of each beam segment into the overall stiffness matrix of the beam body, and its expression is as follows:

[0022] .

[0023] Further, S3 specifically comprises the following sub-steps:

[0024] S301, constructing a deformation matrix ; wherein v i is the measured deflection of each node, positive upwards; θ i is the measured rotation angle of each node, positive counterclockwise;

[0025] S302, constructing a load matrix ; wherein F i corresponds to the concentrated external load acting on the node in the vertical plane, including the support reaction, positive upwards; M i corresponds to the external bending moment acting on the node, positive counterclockwise;

[0026] S303, combining the overall stiffness matrix K obtained in S2 to establish the balance equation KU=F.

[0027] Further, S4 specifically comprises the following sub-steps:

[0028] S401, using a well-posed solution strategy to pre-determine the bending stiffness EI(n) of at least one beam segment as a known quantity, or additionally measuring the rotation angle θ j of at least one node as a known input, reducing the total number of unknowns to no more than 2n+2, converting the equation set into a well-posed equation set, and directly solving to obtain the unique solution of each segment bending stiffness EI(1)~ EI(n);

[0029] S402, using an over-determined solution strategy to additionally measure the rotation angles θ i of at least two different nodes.j And as the known input, the total number of unknowns is at least one less than the total number of equations, resulting in the transformation of the equation set into an over-determined equation set;

[0030] S403, for the over-determined equation set formed in S402, the least square method, QR decomposition method or SVD decomposition method is used to solve, and the optimal estimated value of the bending stiffness EI(1)~ EI(n) of each section is obtained.

[0031] Further, S7 specifically includes the following sub-steps:

[0032] S701, for the homogeneous beam body, based on the edge yield criterion, the relationship is established, and the minimum beam section bending stiffness EI min The maximum bearing moment M max of the section is calculated, and the formula is:

[0033] ; Wherein I is the moment of inertia of the section, h c is the maximum distance from the neutral axis to the edge of the beam, f y is the yield strength of the material, E is the elastic modulus of the material, EI min is the minimum beam section stiffness identified;

[0034] The maximum bearing capacity F max of the beam body is calculated in combination with the boundary conditions and the loading condition; max When three-point loading is used and the weakest section is located at the midspan, the maximum value F of the resultant force of the two loading points is:

[0035] ; Wherein L is the beam length;

[0036] S702, for non-homogeneous beam body, such as three-point loading reinforced concrete rectangular beam, based on the specific relationship between the section bending stiffness EI and the bending moment M and the section balance condition, the relationship equation containing the effective height of the section and the steel area is established.

[0037] Further, the balance equation of the section force and the bending moment in S702 is as follows:

[0038] ;

[0039] ; Wherein E c is the elastic modulus of the concrete, b is the beam width, φ is the section curvature, E s is the elastic modulus of the steel, A s is the total area of the tensile steel, and M is the bending moment of the section.

[0040] Further, the relationship between the section bending stiffness EI and the section bending moment M in S702 is established as follows: ,Will Substituting the given relation, we get:

[0041] Where α is the distance from the center of the tensile reinforcement to the bottom surface of the beam, and c is the distance from the neutral axis to the top surface of the beam.

[0042] Furthermore, consider c and A s As an unknown, combined with the identified minimum beam segment flexural stiffness EI min Through relational formulas and The area A of the tensile reinforcement is obtained by solving the problem. s ;

[0043] Based on the obtained A s The maximum bearing bending moment M of the calculated section max The maximum bearing capacity F of the beam is calculated by combining boundary conditions and loading conditions. max ,get:

[0044] .

[0045] The beneficial effects of this invention are:

[0046] (1) This invention establishes a physical inversion mechanism from structural bending stiffness to key parameters of cross-sectional bearing capacity. By identifying the minimum stiffness at the weakest point of the beam, and combining the equations of mechanics of materials and cross-sectional equilibrium, it is possible to reverse-calculate hidden parameters such as the area of ​​internal steel reinforcement that are difficult to measure directly. Then, the exact bearing capacity value can be calculated through these parameters, which solves the problem that existing methods cannot establish a quantitative mapping relationship between stiffness degradation and remaining bearing capacity.

[0047] (2) By constructing the overall stiffness matrix and solving the equilibrium equation, this invention can obtain the specific distribution of bending stiffness along the beam length, rather than just obtaining an equivalent overall stiffness. This method can not only determine whether the beam is damaged, but also accurately point out which section is damaged and how severe the damage is. Compared with the modal parameter identification method based on frequency and mode shape, this method is more sensitive and accurate in identifying the local stiffness weakening area.

[0048] (3) In view of the difficulty of solving equations caused by the limited number of measuring points in actual engineering, this invention proposes a systematic mathematical solution strategy. When there are few measuring points, the equations are transformed into well-posed equations by using known intact beam segments or adding a small amount of rotation information to ensure that there is a unique solution. When there are many measuring points, the optimal solution is obtained by using the least squares method, QR decomposition or SVD decomposition. The redundant data is effectively utilized to improve the noise resistance and accuracy of identification, and overcomes the defects of existing methods in the lack of a unified mechanism for measuring point layout and data processing.

[0049] (4) The application deduces evaluation formulas for different materials, which are suitable for homogeneous material structures such as steel beams and non-homogeneous material structures such as reinforced concrete beams, and especially considers the synergistic effect of concrete and steel bars in the cracking section of the reinforced concrete beam, so that the evaluation model is more in line with the actual stress state, and overcomes the limitation that the traditional method is difficult to accurately evaluate the bearing capacity of the non-homogeneous composite beam body. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0051] Figure 1 A flowchart of a beam body bearing capacity evaluation method based on stiffness distribution identification is provided for the present application.

[0052] Figure 2 A beam body segmentation diagram of a beam body bearing capacity evaluation method based on stiffness distribution identification is provided for the present application.

[0053] Figure 3 A non-homogeneous beam body reinforced concrete beam cracking section diagram of a beam body bearing capacity evaluation method based on stiffness distribution identification is provided for the present application.

[0054] Figure 4 A simply supported steel beam bearing capacity evaluation loading and measuring point arrangement diagram of a beam body bearing capacity evaluation method based on stiffness distribution identification is provided for the present application.

[0055] Figure 5 A simply supported reinforced concrete beam bearing capacity evaluation loading and measuring point arrangement diagram of a beam body bearing capacity evaluation method based on stiffness distribution identification is provided for the present application.

[0056] Figure 6 A terminal device diagram of a beam body bearing capacity evaluation method based on stiffness distribution identification is provided for the present application.

[0057] Figure 7 A readable storage medium diagram of a beam body bearing capacity evaluation method based on stiffness distribution identification is provided for the present application.

[0058] In the figure, 200 is a terminal device, 210 is a memory, 211 is a RAM, 212 is a cache, 213 is a ROM, 214 is a program / utility, 215 is a program module, 220 is a processor, 230 is a bus, 240 is an external device, 250 is an I / O interface, 260 is a network adapter, 300 is a program product. DETAILED DESCRIPTION

[0059] In order to make the objectives, technical solutions and advantages of the present application clearer, further detailed description will be made to the present application in combination with embodiments and drawings, the illustrative embodiments of the present application and the description thereof are only used to explain the present application, and do not limit the present application.

[0060] Embodiment 1

[0061] Reference Figure 1 , the embodiment of the present application provides a beam carrying capacity evaluation method based on stiffness distribution identification, comprising the following steps:

[0062] Step 1: geometrically segment the beam, apply static load on partial nodes step by step, and record the load size, at the same time, measure the deflection information of the nodes between the segments, and selectively measure the rotation angle information of each node;

[0063] Step 2: assemble the overall stiffness matrix K with the bending stiffness EI(n) of each segment of the segmented beam as unknown array;

[0064] Step 3: combine the boundary conditions of the beam, the load and the measuring point information to construct the balance equation KU=F, wherein U is the deformation matrix, and F is the load matrix;

[0065] Step 4: solve the balance equation KU=F to obtain the bending stiffness EI(n) of each segment;

[0066] Step 5: compare the stiffness distribution changes of the beam under different loading levels to judge the linear elasticity of the beam, the more consistent the stiffness of each segment under different loading levels, the better the linear elasticity of the beam; if the linear elasticity is poor, there is a serious damage, and measures should be taken;

[0067] Step 6: on the basis of good linear elasticity of the beam, compare the stiffness distribution under the last loading level with the historical stiffness distribution to judge whether there is new damage and the development of the damage;

[0068] Step 7: according to the information of the beam material, cross-section size and the like, deduce the relationship between the bending stiffness and the key parameters of the carrying capacity (such as the effective height of the cross-section, the steel area and the like), and calculate the carrying capacity M min of the weakest section according to the minimum stiffness EI max identified by the beam segment. max

[0069] The specific steps of step 1 are as follows:

[0070] ​Step 1-1: Displacement sensors are arranged on each node, and the deflection of each node during the loading process is recorded. The displacement sensor can be a pull wire displacement sensor, a top rod displacement sensor, a laser displacement sensor, or a visual-based displacement measurement method. The number of node angle measurements can be determined in step 4.

[0071] Step 1-2: Apply load to part of the nodes (such as one-third point loading of the beam) in stages, and record the load data. The last stage of applied load does not exceed the load under normal working conditions of the beam.

[0072] The specific steps of step 2 are as follows:

[0073] Reference Figure 2 Step 2-1: For the beam in the figure, the beam length is L, which is divided into n beam segments, each with a length of l, and the corresponding bending stiffness is EI(n). The measured vertical displacement and angle of the nodes are v1, v2, v 3… v n+1 and θ1, θ2, θ 3… θ n+1 ; The element stiffness matrix K n of the nth beam segment is established, and its expression is as follows:

[0074] ; Where i and j are the left and right nodes of the beam segment.

[0075] Step 2-2: Assemble the element stiffness matrix of each beam segment into the overall stiffness matrix of the beam, and its expression is as follows:

[0076] ;

[0077] In this embodiment, for a beam with only two segments, the overall stiffness matrix is calculated as follows:

[0078]

[0079] .

[0080] The specific steps of step 3 are as follows:

[0081] Step 3-1: Construct the deformation matrix ; Where v i is the measured deflection of each node, positive upwards; θ i is the measured angle of each node, positive counterclockwise.

[0082] Step 3-2: Construct the load matrix ; Where F i is the concentrated external load acting on the node in the vertical plane, including the support reaction, positive upwards; M iThe external bending moment acting on the corresponding node is positive counterclockwise;

[0083] Step 3-3: Combine the total stiffness matrix K obtained in step 2 to establish the balance equation KU=F.

[0084] The specific steps of step 4 are as follows:

[0085] According to the balance equation in step 3, the total number of equations is 2n+2, and the number of unknowns includes:

[0086] (1) The bending stiffness of each beam segment EI(1), EI(2), EI(3)... EI(n);

[0087] (2) The rotation angles of n+1 nodes (if only the deflection of the node is measured and the rotation angle is not measured);

[0088] (3) The support reaction.

[0089] For example, for a simply supported beam, only the node deflection and the applied load value are measured, the number of unknowns is 2n+3, which is more than the number of equations, resulting in an indeterminate equation without a unique solution. One of the following steps can be used to solve the bending stiffness EI(n) of each segment.

[0090] Step 4-1: Consider the bending stiffness of a certain beam segment as known (such as a certain undamaged segment), or measure an additional rotation angle information, so that the equation is called a well-posed equation, which has a unique solution;

[0091] Step 4-2: Measure the rotation angle information of more than 1 node, the number of unknowns will be less than the number of equations, resulting in an over-determined equation, which can be solved by least squares method, QR decomposition method or SVD decomposition method.

[0092] The specific steps of step 5 are as follows:

[0093] Step 5-1: Organize the stiffness distribution data calculated in step S4 under each level of load, for example, when using three levels of loading, extract the corresponding bending stiffness sequence of each beam segment under the first level of load F1, the second level of load F2 and the third level of load F3, respectively, EI F1 (n), EI F2 (n) and EI F3 (n);

[0094] Step 5-2: Calculate the relative deviation or coefficient of variation of the bending stiffness of the same beam segment under different load levels, for example, for the nth beam segment, calculate the maximum relative error of the stiffness value under each level of load:

[0095] ;

[0096] Step 5-3: Set a linear elasticity determination threshold (e.g. 5%). If all the beam segments' δn are less than the threshold, it is determined that the beam is in linear elastic state, the stiffness identification result is valid, and step S6 is entered; if there is a beam segment whose δn exceeds the threshold, or the stiffness shows a significant downward trend with the increase of load, it is determined that the beam has nonlinear damage or crack development, and further detection measures need to be taken.

[0097] The specific steps of step 6 are as follows:

[0098] Step 6-1: Retrieve the historical health record of the beam to obtain the initial state or the bending stiffness distribution data EI history (n) of the last assessment as the reference data, or use the design theory stiffness or the measured stiffness at the completion acceptance as the reference if there is no historical data;

[0099] Step 6-2: Compare the bending stiffness distribution EI current (n) of the last level load (usually the maximum test load) confirmed valid in step 5 with the reference data EI history (n) segment by segment, and calculate the stiffness degradation rate D:

[0100] ;

[0101] Step 6-3: According to the stiffness degradation rate D n , judge the damage condition. If a beam segment D n is positive and exceeds a preset damage threshold (e.g. 10%), it is determined that the beam segment has new damage or the original damage has developed through accumulation; if D n is within a reasonable measurement error range, it is determined that the regional structure performance is stable.

[0102] The specific steps of step 7 are as follows:

[0103] This embodiment is based on the different materials of the beam and is divided into the following two cases:

[0104] (1) For homogeneous beams, such as steel beams, first deduce the relationship between the cross-sectional bearing capacity M max and the cross-sectional bending stiffness EI; then obtain the cross-sectional bearing capacity M min according to the minimum bending stiffness EI max identified by the beam; finally, combined with the boundary conditions and loading conditions, the maximum bearing capacity F max of the beam is obtained. This embodiment takes a three-point loading of a simply supported rectangular steel beam as an example. Based on the edge yield criterion, when the cross-section edge yields, the maximum bending moment M max that the weakest cross-section of the beam can withstand is:

[0105] Where I is the moment of inertia of the cross section, h is the height of the cross section, and f is the moment of inertia of the cross section. y Let E be the yield strength of the steel, and E be the elastic modulus of the steel, EI min To identify the minimum beam segment stiffness;

[0106] Calculate the maximum bearing capacity F of the beam by combining boundary conditions and loading conditions. max When the weakest section is located at the mid-span:

[0107] Where L is the beam length.

[0108] (2) For non-homogeneous beams, such as reinforced concrete beams, first establish the specific relationship between the flexural stiffness EI of the section and the bending moment M, and then combine the section equilibrium conditions with EI. min Calculate the area A of the tensile reinforcement. s Thus, the maximum bearing capacity M of the cross section is obtained. max Finally, the bearing capacity F of the beam is obtained by combining the boundary conditions and loading conditions. max This embodiment uses a simply supported reinforced concrete rectangular beam with three-point loading as an example for illustration. (Refer to...) Figure 3 The cracked section of a reinforced concrete beam is shown in the figure. In the figure, h is the beam height, c is the distance from the neutral axis to the top surface of the beam, and a is the distance from the center of the tensile reinforcement to the bottom surface of the beam. Ignoring the effects of the compression zone reinforcement and the tension zone concrete after cracking, the equilibrium equations for the section forces and bending moments are:

[0109] ;

[0110] ; where E c Let φ be the elastic modulus of concrete, b be the beam width, φ be the cross-sectional curvature, and E be the cross-sectional curvature. s Let A be the elastic modulus of the reinforcing steel. s M represents the total area of ​​the tensile reinforcement, and M represents the bending moment borne by the section.

[0111] Establish the relationship between the flexural stiffness EI of the section and the bending moment M that the section can withstand. ,Will Substituting the given relation, we get:

[0112] Where α is the distance from the center of the tensile reinforcement to the bottom surface of the beam, and c is the distance from the neutral axis to the top surface of the beam.

[0113] Place c and A s Treating it as an unknown, and combining it with the minimum beam segment stiffness EI obtained from the identification. min Through relational formulas and The area A of the tensile reinforcement is obtained by solving the problem. s This leads to the maximum bearing bending moment M of the cross section.max The beam bearing capacity is determined by combining boundary conditions and loading conditions, such as when the weakest section is located at the mid-span. max (the sum of the two loading forces) is .

[0114] Example 2

[0115] In this embodiment, a simply supported steel beam with a rectangular cross-section is selected as the evaluation object. The calculated length L = 2.1m, the beam width b and beam height h are 120mm and 220mm respectively, the elastic modulus E = 2.1 × 10¹¹ Pa, and the yield strength f y =235MPa. After a period of use, some sections suffered damage, and their load-bearing capacity is unknown. The load-bearing capacity is now evaluated according to the present invention, the steps of which are as follows: Figure 1 As shown, the details are as follows:

[0116] Step 1: Divide the beam into 6 segments as follows Figure 4 As shown. Three loading levels were applied at the midpoint of the span, with loading levels of 100N, 250N, and 500N respectively. It was observed that the portion of the beam near the ends showed no damage; therefore, the bending stiffness of this section near the ends was taken as a known value: EI(1) = 2.236 × 10⁻⁶. 7 Nm. Deflection information of nodes between segments is measured after each loading.

[0117] Step 2: Assemble the overall stiffness matrix K by taking the bending stiffness EI(n) of each segment after the beam is divided into segments as unknowns.

[0118] Step 3: Construct the equilibrium equation KU=F by combining the beam boundary conditions, loads and measuring point information, where U is the deformation matrix and F is the load matrix;

[0119] Step 4: Solve the equilibrium equation KU=F to obtain the flexural stiffness of each segment under each loading level.

[0120] The stiffness of each segment under the first-level loading is:

[0121] EI(2) = 2.256 × 10 7 Nm, EI(3) = 2.150 × 10 7 Nm, EI(4) = 2.151 × 10 7 Nm, EI(5) = 2.156 × 10 7 Nm, EI(6) = 2.225 × 10 7 Nm.

[0122] The stiffness of each segment under the second-level loading is:

[0123] EI(2) = 2.259 × 10 7 Nm, EI(3) = 2.155 × 107 Nm, EI(4) = 2.155 × 10 7 Nm, EI(5) = 2.159 × 10 7 Nm, EI(6) = 2.229 × 10 7 Nm.

[0124] The stiffness of each segment under the third-level loading is:

[0125] EI(2) = 2.258 × 10 7 Nm, EI(3) = 2.152 × 10 7 Nm, EI(4) = 2.152 × 10 7 Nm, EI(5) = 2.158 × 10 7 Nm, EI(6) = 2.227 × 10 7 Nm. The minimum stiffness is near the mid-span, i.e., EImin = 2.152 × 10⁻⁶. 7 Nm.

[0126] Step 5: Compare the changes in the stiffness distribution of the beam under different loading levels. It is found that the identification results are relatively consistent under each loading level, and the linear elasticity of the beam is good.

[0127] Step 6: Assuming the beam's linear elasticity is relatively good, compare the stiffness distribution under the last loading stage with the historical stiffness distribution to determine if there is new damage and its development. In this case, there are no historical test records, so no comparison is made at this stage.

[0128] Step 7: Based on the beam material, cross-sectional dimensions, and other information, derive the relationship between key parameters of flexural stiffness and bearing capacity (such as effective cross-sectional height, reinforcement area, etc.). Refer to the formula for the calculation method:

[0129] .

[0130] By identifying the minimum stiffness EI of the beam segment min Determine the bearing capacity M max =2.1893×10 5 Nm. The maximum bearing capacity F is obtained by combining boundary conditions and loading conditions. max =4M max / L=417kN.

[0131] The load-bearing capacity of the beam was tested in the laboratory and the actual value of its load-bearing capacity was 436kN. It can be seen that the error of the evaluation result according to the present invention is 4.36%, which meets the engineering requirements.

[0132] Example 3

[0133] This embodiment selects a rectangular reinforced concrete simply supported beam as the evaluation object. The beam length is 2.2m, the calculated length L=2.1m, the beam width b=120mm, the beam height h=220mm, and the concrete elastic modulus E. c =3.0×10¹ 0 Pa, elastic modulus of steel bar E s =2.0 × 10¹¹ Pa. After a period of use, the tensile reinforcement corroded, leading to a reduction in load-bearing capacity. The load-bearing capacity is now evaluated according to the present invention, the steps of which are as follows: Figure 1 As shown, the details are as follows:

[0134] Step 1: Divide the beam into 6 segments as follows Figure 5 As shown, a three-point loading method was adopted, with three loading levels: 5kN, 10kN, and 20kN. After each loading, the deflection and rotation angle of the nodes between each segment were measured.

[0135] Step 2: Assemble the overall stiffness matrix K by taking the bending stiffness EI(n) of each segment after the beam is divided into segments as unknowns.

[0136] Step 3: Construct the equilibrium equation KU=F by combining the beam boundary conditions, loads and measuring point information, where U is the deformation matrix and F is the load matrix;

[0137] Step 4: Find the optimal solution of the equilibrium equation KU=F using the least squares method to obtain the bending stiffness of each segment under each loading level.

[0138] The stiffness of each segment under the first-level loading is:

[0139] EI(1) = 1.7310 × 10 6 Nm, EI(2) = 1.3040 × 10 6 Nm, EI(3) = 1.1440 × 10 6 Nm, EI(4) = 1.1430 × 10 6 Nm, EI(5) = 1.3055 × 10 6 Nm, EI(6) = 1.7205 × 10 6 Nm.

[0140] The stiffness of each segment under the second-level loading is:

[0141] EI(1) = 1.7205 × 10 6 Nm, EI(2) = 1.2950 × 10 6 Nm, EI(3) = 1.1460 × 10 6 Nm, EI(4) = 1.1451 × 10 6Nm, EI(5) = 1.3055 × 10 6 Nm, EI(6) = 1.7200 × 10 6 Nm.

[0142] The stiffness of each segment under the third-level loading is:

[0143] EI(1) = 1.7215 × 10 6 Nm, EI(2) = 1.3050 × 10 6 Nm, EI(3) = 1.1450 × 10 6 Nm, EI(4) = 1.1450 × 10 6 Nm, EI(5) = 1.3050 × 10 6 Nm, EI(6) = 1.7215 × 10 6 Nm.

[0144] The minimum stiffness is located near the mid-span, i.e., EImin = 1.1450 × 10⁻⁶. 6 Nm.

[0145] Step 5: Compare the changes in the stiffness distribution of the beam under different loading levels. It is found that the identification results are relatively consistent under each loading level, and the linear elasticity of the beam is good.

[0146] Step 6: Assuming the beam's linear elasticity is relatively good, compare the stiffness distribution under the last loading stage with the historical stiffness distribution to determine if there is new damage and its development. In this case, there are no historical test records, so no comparison is made at this stage.

[0147] Step 7: Based on the beam material, cross-sectional dimensions and other information, derive the relationship between the key parameters of bending stiffness and bearing capacity (such as the effective height of the cross-section, the area of ​​the reinforcing bars, etc.). See Example 1 for the derivation process.

[0148] Then, by combining the cross-sectional equilibrium equations, the height of the concrete compression zone is obtained as c = 61.80 mm, and the area of ​​the tensile reinforcement is A. s =273mm 2 The bearing capacity M of the weakest section was calculated. max =16.45 kN·m. Based on the boundary conditions and loading conditions of the beam, its maximum bearing capacity (the sum of the two concentrated loading forces) F is obtained. max =6M max / L=47.00kN.

[0149] The load-bearing capacity of the beam was tested in the laboratory, and the true value of its load-bearing capacity, which is the sum of the two concentrated loading forces, was 44 kN. It can be seen that the evaluation result according to the present invention has an error of 6.82%. Considering that reinforced concrete material itself has significant heterogeneity and dispersion, and that the distribution of cracks in the damaged beam is random, this error range is within the reasonable allowable range for the identification of damage in engineering structures. The present invention can effectively evaluate the load-bearing capacity level of damaged structures and provide reliable data support for engineering maintenance and reinforcement.

[0150] Example 4

[0151] refer to Figure 6 Based on Example 1, this example proposes a terminal device for a beam bearing capacity assessment method based on stiffness distribution identification. The terminal device 200 includes at least one memory 210, at least one processor 220, and a bus 230 connecting different platform systems.

[0152] The memory 210 may include a readable medium in the form of volatile memory, such as RAM 211 and / or cache memory 212, and may further include ROM 213.

[0153] The memory 210 also stores a computer program that can be executed by the processor 220, causing the processor 220 to perform any of the above-described applications of the beam bearing capacity assessment method based on stiffness distribution identification in this application embodiment. The specific implementation method and the achieved technical effects are consistent with those described in the above-described application embodiments, and some details will not be repeated here. The memory 210 may also include a program / utility 214 having a set (at least one) of program modules 215. Such program modules include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment.

[0154] Accordingly, processor 220 can execute the aforementioned computer program, as well as executable program / utility 214.

[0155] Bus 230 can represent one or more of several types of bus structures, including a memory bus or memory controller, peripheral bus, graphics acceleration port, processor, or a local bus using any of the various bus structures.

[0156] Terminal device 200 can also communicate with one or more external devices 240, such as keyboards, pointing devices, Bluetooth devices, etc., and with one or more devices capable of interacting with it, and / or with any device that enables it to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication can be performed via I / O interface 250. Furthermore, terminal device 200 can communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via network adapter 260. Network adapter 260 can communicate with other modules of terminal device 200 via bus 230. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with terminal device 200, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0157] Example 5

[0158] This embodiment proposes a readable storage medium for a beam bearing capacity assessment method based on stiffness distribution identification. The computer-readable storage medium stores instructions that, when executed by a processor, implement any of the above-mentioned beam bearing capacity assessment methods based on stiffness distribution identification. The specific implementation method and the technical effects achieved are consistent with those described in the above-mentioned application embodiments, and some details will not be repeated.

[0159] Figure 7 The present embodiment illustrates a program product 300 for implementing the above-described applications. This product may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may run on a terminal device, such as a personal computer. However, the program product 300 of the present invention is not limited thereto. In this embodiment, the readable storage medium may be any tangible medium containing or storing a program that may be used by or in conjunction with an instruction execution system, apparatus, or device. The program product 300 may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disc read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0160] Computer-readable storage media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof. Program code for performing operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on a user computing device, partially on a user device, as a standalone software package, partially on a user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing devices can be connected to user computing devices via any type of network, including local area networks (LANs) or wide area networks (WANs), or they can be connected to external computing devices (e.g., via the Internet using an Internet service provider).

[0161] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the bearing capacity of beams based on stiffness distribution identification, characterized in that, Includes the following steps: S1. Geometrically segment the beam to be evaluated, apply static loads to some nodes step by step, record the load magnitude, measure the deflection information of the nodes between each segment, and selectively measure the rotation information of each node. S2. Using the bending stiffness EI(n) of each segment after dividing the beam into segments as unknowns, construct the overall stiffness matrix K of the beam; S3. Combining the beam boundary conditions, deformation matrix U, and load matrix F, construct the equilibrium equation KU=F; S4. Solve the equilibrium equations to obtain the distribution of the flexural stiffness EI(n) of each segment of the beam along the beam length, i.e., the flexural stiffness distribution, and identify the segment with the minimum flexural stiffness EI. min ; S5. Compare the changes in the bending stiffness distribution of the beam under different loading levels to determine the linear elasticity of the beam. If the bending stiffness of each segment is consistent under different loading levels, the linear elasticity of the beam is considered to be good; otherwise, it is considered to have serious damage. S6. On the basis of good linear elasticity of the beam, compare the bending stiffness distribution under the last loading stage with the historical bending stiffness distribution to determine whether there is new damage and the development of damage. S7. Based on the beam material and cross-sectional dimensions, derive the relationship between key parameters of flexural stiffness and bearing capacity, using the minimum flexural stiffness EI of the beam segment. min The bearing capacity M of the weakest section is calculated. max The maximum bearing capacity F is obtained by combining the boundary conditions and loading conditions. max .

2. The beam bearing capacity assessment method based on stiffness distribution identification according to claim 1, characterized in that, S1 specifically includes the following sub-steps: S101. Displacement sensors are arranged at each node. The displacement sensors acquire data using methods such as wire displacement gauges, push rod displacement gauges, laser displacement gauges, or vision-based displacement measurement methods. S102. Apply loads to some nodes, using a graded loading method, with the last grade of the applied load not exceeding the load under normal working conditions of the beam, and simultaneously record the deflection data and selectively measured rotation data of each node during the loading process.

3. The beam bearing capacity assessment method based on stiffness distribution identification according to claim 1, characterized in that, S2 specifically includes the following sub-steps: S201. Divide a beam of length L into n segments, each segment being of length l and having a corresponding bending stiffness of EI(n). The vertical displacement and rotation angle of each node are v1, v2, and v3, respectively. 3… v n+1 and θ1, θ2, θ 3… θ n+1 Establish the element stiffness matrix K for the nth beam segment. n Its expression is as follows: ； Where i and j are the left and right nodes of the beam segment; S202, calculate the element stiffness matrix K for each beam segment. n The overall stiffness matrix of the assembled beam is expressed as follows: 。 4. The beam bearing capacity assessment method based on stiffness distribution identification according to claim 1, characterized in that, S3 specifically includes the following sub-steps: S301, Constructing the deformation matrix ;where v i θ represents the measured deflection at each node, with upward being positive; i The measured rotation angles at each node are represented, with counterclockwise being positive. S302, Construct the load matrix ;where F i Concentrated external loads acting on nodes in the vertical plane, including support reactions, are positive upwards; M i The external bending moment acting on the corresponding node is positive when it is counterclockwise. S303. Combining the overall stiffness matrix K obtained in S2, establish the equilibrium equation KU=F.

5. The beam bearing capacity assessment method based on stiffness distribution identification according to claim 1, characterized in that, S4 specifically includes the following sub-steps: S401. Employ a well-posed solution strategy, pre-determine the flexural stiffness EI(n) of at least one beam segment as a known quantity, or additionally measure the rotation angle θ of at least one node. j And as known input, the total number of unknowns is reduced to no more than 2n+2, the system of equations is transformed into a well-posed system of equations, and the unique solution of the bending stiffness EI(1)~EI(n) of each segment is obtained directly; S402. Employ an overdetermined solution strategy and additionally measure the rotation angle θ at at least two different nodes. i and θ j And as known input, the total number of unknowns is at least one less than the total number of equations, causing the system of equations to be transformed into an overdetermined system of equations; S403. For the overdetermined equation set formed in S402, the least squares method, QR decomposition method or SVD decomposition method are used to solve the equation set to obtain the optimal estimated values ​​of the bending stiffness EI(1)~EI(n) of each segment.

6. The beam bearing capacity assessment method based on stiffness distribution identification according to claim 1, characterized in that, S7 specifically includes the following sub-steps: S701. For homogeneous beams, establish relationships based on the edge yield criterion, and utilize the identified minimum beam segment flexural stiffness EI. min Calculate the maximum bearing bending moment M of the section max The formula is: Where I is the moment of inertia of the cross section, h c f is the maximum distance from the neutral axis to the edge of the beam. y E is the yield strength of the material, and E is the elastic modulus of the material. min To identify the minimum beam segment stiffness; Calculate the maximum bearing capacity F of the beam by combining boundary conditions and loading conditions. max When using three-point loading, the maximum resultant force F at the two loading points is when the weakest section is located at the mid-span. max for: Where L is the beam length; S702. For non-homogeneous beams, establish a relational equation that includes the effective height of the section and the area of ​​the reinforcing bars, based on the specific relationship between the section bending stiffness EI and the bending moment M and the section equilibrium conditions.

7. The beam bearing capacity assessment method based on stiffness distribution identification according to claim 6, characterized in that, The equilibrium equations for section force and bending moment in S702 are established as follows: ； ; where E c Let φ be the elastic modulus of concrete, b be the beam width, φ be the cross-sectional curvature, and E be the cross-sectional curvature. s Let A be the elastic modulus of the reinforcing steel. s M represents the total area of ​​the tensile reinforcement, and M represents the bending moment borne by the section.

8. The beam bearing capacity assessment method based on stiffness distribution identification according to claim 7, characterized in that, In S702, the relationship between the flexural stiffness EI of the section and the bending moment M borne by the section is established. ,Will Substituting the given relation, we get: Where α is the distance from the center of the tensile reinforcement to the bottom surface of the beam, and c is the distance from the neutral axis to the top surface of the beam.

9. The beam bearing capacity assessment method based on stiffness distribution identification according to claim 7, characterized in that, Place c and A s As an unknown, combined with the identified minimum beam segment flexural stiffness EI min Through relational formulas and The area A of the tensile reinforcement is obtained by solving the problem. s ; Based on the obtained A s The maximum bearing bending moment M of the calculated section max The maximum bearing capacity F of the beam is calculated by combining boundary conditions and loading conditions. max ,get: 。

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