A method for evaluating the bearing capacity of a reinforced concrete beam

Abstract

The present application relates to a kind of reinforced concrete beam bearing capacity evaluation method applied to the field of civil engineering technology, including the finite element modeling of the beam to be evaluated, the uniform damage of the tensile reinforcement is characterized by different degrees of reduction to tensile reinforcement area, the bending moment displacement curve at loading point under no-damage condition and different damage conditions is calculated based on finite element model, the corresponding tensile reinforcement yield bending moment under each condition and the slope of the elastic stage of each bending moment displacement curve are obtained according to the bending moment displacement curve under each condition, etc. The reinforced concrete beam bearing capacity evaluation method in the present application, the bearing capacity of reinforced concrete beam with uniform damage is quantitatively evaluated by combining simulation data and field measured data, has the advantages of clear concept and simple calculation, facilitates the technical personnel in the field to quickly and accurately evaluate the bearing capacity of reinforced concrete beam, and can provide strong support for the bearing capacity evaluation of in-service reinforced concrete bridge.

Description

TECHNICAL FIELD

[0001] The application relates to a bearing capacity evaluation method, in particular to a reinforced concrete beam bearing capacity evaluation method applied to the technical field of civil engineering. BACKGROUND

[0002] For civil engineering structures, especially bridge structures, their bearing capacity will continuously degrade under the action of environment and load, and when the load exceeds the bearing capacity, the bridge will collapse, causing a tragedy of car damage and human death. Therefore, it is of great theoretical and practical significance to accurately evaluate the bearing capacity of the in-service bridge. Therefore, a large number of scholars at home and abroad have carried out a large amount of research on the bearing capacity evaluation method of reinforced concrete beams.

[0003] The application patent with the publication number CN110414580A discloses a reinforced concrete deep beam bearing capacity evaluation method based on a random forest algorithm. The application can directly give the shear strength of the node according to the input related parameters, avoiding the problems of high time consumption and high cost of the traditional experimental method, and avoiding the problems of multiple assumptions, unclear mechanism and complex calculation process caused by the theoretical analysis method.

[0004] The application patent with the publication number CN118194403A discloses a reinforced concrete beam bending bearing capacity calculation method under different cooling modes. The calculation method proposed in the application can accurately predict the bending bearing capacity of the reinforced concrete beam under two different cooling modes of water spray cooling and natural cooling in actual fire, and can provide a theoretical basis for the repair and reinforcement of the reinforced concrete beam after fire extinguishing by water spray.

[0005] However, the current theoretical calculation method has problems of large number of parameters, inconvenient parameter selection, complex calculation and insufficient calculation result precision, and the field load test has problems of multiple loading conditions and only qualitative evaluation of the bearing capacity without quantifying the specific value. Therefore, the application provides a reinforced concrete beam bearing capacity evaluation method. SUMMARY

[0006] In view of the above prior art, the technical problems to be solved by the application are that the current theoretical calculation method has problems of large number of parameters, inconvenient parameter selection, complex calculation and insufficient calculation result precision, and the field load test has problems of multiple loading conditions and only qualitative evaluation of the bearing capacity without quantifying the specific value.

[0007] To solve the above problems, the application provides a reinforced concrete beam bearing capacity evaluation method, which comprises the following steps:

[0008] S1, finite element modeling is performed on the beam to be evaluated to obtain a finite element model;

[0009] S2. In the finite element model, the area of ​​the tensile reinforcement is reduced to different degrees to characterize the uniform damage of the tensile reinforcement, thereby obtaining different damage conditions D1, D2, D3...D n ;

[0010] S3. Calculate the undamaged condition D0 and different damage conditions D1, D2, D3...D based on the finite element model. n The moment-displacement curve at the lower loading point;

[0011] S4. Based on the moment-displacement curves under each working condition, obtain the corresponding yield moments of the tensile reinforcement M0, M1, M2, M3...M under each working condition. n And the slopes K0, K1, K2, K3...K of the elastic stage of each moment-displacement curve. n ;

[0012] S5, for [K0, K1, K2, K3...K n ] and [M0, M1, M2, M3...M n By fitting the equation, we obtain the linear equation:

[0013] y = Kx + b (1)

[0014] In the formula, y is the dependent variable, x is the independent variable, and K and b are constants;

[0015] S6. Conduct a load test on the beam to be evaluated to obtain the slope K of the elastic stage of the moment-displacement curve at the loading point. p , will K p Substituting the y-value into formula (1) as the independent variable, the calculated y-value is the yield moment M of the section at the loading point of the beam to be evaluated. p The calculation formula is:

[0016] M p =K×K p +b (2).

[0017] The above-mentioned method for assessing the load-bearing capacity of reinforced concrete beams combines simulated data and on-site measured data to quantitatively assess the load-bearing capacity of reinforced concrete beams with uniform damage. This method has the advantages of clear concepts and simple calculations.

[0018] As a further improvement to this application, in step S1, to ensure that the evaluation results are on the safe side, in the finite element model, the yield strength of the tensile steel bar is taken as the minimum value of the measured value, and the elastic modulus of the steel bar and concrete is taken as the maximum value of the measured value.

[0019] As a further improvement of this application, the moment-displacement curve in step S3 includes an elastic stage and a yielding stage.

[0020] As a further improvement of the present application, the step S3 further comprises the following content: comparing the elastic stage of the bending moment displacement curve under the intact working condition calculated based on the finite element model with the elastic stage of the bending moment displacement curve of the intact beam, to ensure the accuracy of the parameters and calculation in the finite element model.

[0021] As a further improvement of the present application, in the step S3 of calculating the bending moment displacement curve at the loading point based on the finite element model, the loading mode can adopt single-point or multi-point vertical loading, and the loading point and the displacement measurement point can be at the same cross-section position or different cross-section positions.

[0022] As a further improvement of the present application, the method is suitable for the bearing capacity evaluation of the steel reinforced concrete beam under the condition of uniform damage of the tensile steel bars.

[0023] In summary, the steel reinforced concrete beam bearing capacity evaluation method in the present application quantitatively evaluates the bearing capacity of the steel reinforced concrete beam with uniform damage by combining the simulation data and the field measurement data, has the advantages of clear concept and simple calculation, facilitates the rapid and accurate evaluation of the bearing capacity of the steel reinforced concrete beam by the person skilled in the art, and can provide strong support for the bearing capacity evaluation of the in-service steel reinforced concrete bridge. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The method flow chart of the steel reinforced concrete beam bearing capacity evaluation method in the first embodiment of the present application;

[0025] Figure 2 The cross-section structure schematic diagram of the simply supported T beam in the second embodiment of the present application;

[0026] Figure 3 The bending moment displacement curve diagram of the loading point under different damage working conditions simulated by the finite element model in the second embodiment of the present application;

[0027] Figure 4 The fitting effect diagram of the elastic stage slope of the bending moment displacement curve of the loading point under different damage working conditions and the yield bending moment in the second embodiment of the present application;

[0028] Figure 5 The bending moment displacement curve diagram of the loading point of the simply supported T beam in the second embodiment of the present application. DETAILED DESCRIPTION

[0029] The two embodiments of the present application will be described in detail below with reference to the drawings.

[0030] First embodiment:

[0031] Figure 1 A steel reinforced concrete beam bearing capacity evaluation method is shown, comprising the following steps:

[0032] S1, finite element modeling is performed on the beam to be evaluated to obtain a finite element model, to ensure that the evaluation result is on the safe side, in the finite element model, the yield strength of the tensile reinforcement is the minimum value of the measured value, and the elastic modulus of the reinforcement and the concrete is the maximum value of the measured value;

[0033] S2, in the finite element model, the tensile reinforcement area is reduced to different degrees to represent uniform damage of the tensile reinforcement, thereby obtaining different damage conditions D1, D2, D3...D n ;

[0034] S3, based on the finite element model, the bending moment displacement curve at the loading point under the non-damage condition D0 and the different damage conditions D1, D2, D3...D n is calculated, the bending moment displacement curve includes an elastic stage and a yield stage, the loading mode can adopt single-point or multi-point vertical loading, the loading point and the displacement measuring point can be the same section position or different section positions, and the bending moment displacement curve under the non-damage condition calculated based on the finite element model is compared with the measured bending moment displacement curve of the non-damage beam (only the elastic stage is compared), to ensure the accuracy of the parameters and the calculation in the finite element model;

[0035] S4, the corresponding tensile reinforcement yield bending moment M0, M1, M2, M3...M n and the slope K0, K1, K2, K3...K n of each bending moment displacement curve in each condition are obtained according to the bending moment displacement curve in each condition;

[0036] S5, [K0, K1, K2, K3...K n ] and [M0, M1, M2, M3...M n ] are fitted to obtain a linear equation:

[0037] y=Kx+b (1)

[0038] In the formula, y is the dependent variable, x is the independent variable, K and b are constants;

[0039] S6, load test is performed on the beam to be evaluated to obtain the slope K p of the elastic stage of the bending moment displacement curve at the loading point; p K p is substituted into formula (1) as the independent variable, and the calculated y value is the section yield bending moment M p at the loading point of the beam to be evaluated, and the calculation formula is:

[0040] M p =K×K p +b (2).

[0041] The method for assessing the load-bearing capacity of reinforced concrete beams in this application quantitatively evaluates the load-bearing capacity of reinforced concrete beams with uniform damage by combining simulation data and field measured data. It has the advantages of clear concept and simple calculation, which makes it convenient for those skilled in the art to quickly and accurately assess the load-bearing capacity of reinforced concrete beams and can provide strong support for the load-bearing capacity assessment of in-service reinforced concrete bridges.

[0042] It should be noted that the load-bearing capacity assessment method in this application is mainly applicable to the load-bearing capacity assessment of tensile reinforcement in reinforced concrete beams under conditions of uniform damage (e.g., uniform corrosion).

[0043] Second implementation method:

[0044] Please refer to Figures 2-5 Taking a beam from a simply supported reinforced concrete T-beam bridge as an example, this paper illustrates the method for evaluating the bearing capacity of reinforced concrete beams in the first embodiment. The simply supported T-beam is 19.96m long, has a calculated span of 19.50m, and its cross-sectional dimensions are as follows. Figure 2 As shown, the concrete strength grade of this beam is C30, and the main reinforcement uses HRB335 steel bars. Currently, the tensile reinforcement of the beam exhibits a certain degree of uniform corrosion damage. A quantitative assessment of the beam's load-bearing capacity is required, and the assessment method is as follows:

[0045] 1. The load-displacement response of the beam under different damage levels D0, D1, D2, and D3 was calculated using a finite element model. Damage was achieved by reducing the area of ​​the tensile reinforcement. The loading method was three-point loading, and the displacement measurement points were at the loading points. When performing the calculation using the finite element model, the yield strength of the tensile reinforcement was taken as the minimum measured value, and the elastic modulus of the reinforcement and concrete was taken as the maximum measured value. The moment-displacement curves at the loading points under different damage levels obtained by the finite element model calculation are shown below. Figure 3 As shown;

[0046] 2. Based on the moment-displacement curves under different damage degrees D0, D1, D2, and D3, the corresponding elastic stage curve slopes K0 = 36.64 kN.m / mm, K1 = 33.52 kN.m / mm, K2 = 29.84 kN.m / mm, K3 = 25.07 kN.m / mm and the yield moments at the loading points M0 = 2384 kN.m, M1 = 2107 kN.m, M2 = 1830 kN.m, M3 = 1467 kN.m were obtained. These curves were then fitted, and the fitting results are as follows: Figure 4 As shown, with a coefficient of determination (R-square) of 0.9987, the equation of the straight line is obtained: M p =78.67K p -513;

[0047] 3. A load test was conducted on the beam, and the bending moment-displacement curves at the loading points were obtained as follows:Figure 5 The slope K of the elastic stage of the bending moment displacement curve is obtained according to the graph p = 31.75 kN.m / mm, which is substituted into the above linear equation to obtain the yield bending moment M of the loading point of the beam p = 1984.8 kN.m.

[0048] The yield bending moment obtained by using the method is 1984.8 kN.m, and the measured value is 1961 kN.m, with an error of 1.21%.

[0049] In combination with the current actual demand, the above-mentioned embodiments adopted by the application are not limited thereto, and various changes made within the knowledge range of those skilled in the art without departing from the concept of the application still fall within the protection scope of the application.

Claims

1. A method of assessing the load carrying capacity of a reinforced concrete beam, characterised in that, The method comprises the following steps: S1, finite element modeling is performed on the beam to be evaluated to obtain a finite element model; S2, in the finite element model, the area of the tensile reinforcement is reduced to different degrees to represent uniform damage of the tensile reinforcement, thereby obtaining different damage conditions D1, D2, D3...Dn; S3, based on the finite element model, the bending moment-displacement curve at the loading point under the non-damage condition D0 and the different damage conditions D1, D2, D3...Dn is calculated; S4, the corresponding tensile reinforcement yield bending moment M0, M1, M2, M3...Mn under each condition and the slope K0, K1, K2, K3...Kn of the elastic stage of each bending moment-displacement curve are obtained according to the bending moment-displacement curve under each condition; S5, the linear equation is used to fit [K0, K1, K2, K3...Kn] and [M0, M1, M2, M3...Mn], and the linear equation is y=Kx+b (1) In the formula, y is the dependent variable, x is the independent variable, K and b are coefficients, and K and b are determined by fitting; S6, load test is performed on the beam to be evaluated to obtain the slope Kp of the bending moment-displacement curve at the loading point, and Kp is taken as the independent variable to substitute into formula (1), and the calculated y value is the section yield bending moment M of the loading point of the beam to be evaluated, and the calculation formula is: In the step S1, in order to ensure that the evaluation result is safe, the yield strength of the tensile reinforcement in the finite element model is the minimum value of the measured value, and the elastic modulus of the reinforcement and the concrete is the maximum value of the measured value. M p = K x K p + b (2).

2. The method of claim 1, wherein, The bending moment-displacement curve in the step S3 includes an elastic stage and a yield stage.

3. The method of claim 1, wherein, The step S3 further comprises the following content: comparing the elastic stage of the bending moment-displacement curve under the non-damage condition calculated based on the finite element model with the elastic stage of the measured bending moment-displacement curve of the non-damage beam to ensure the accuracy of the parameters in the finite element model and the calculation.

4. The method of claim 3, wherein, In the step S3, when the bending moment-displacement curve at the loading point is calculated based on the finite element model, the loading mode adopts single-point or multi-point vertical loading.

5. The method of claim 1, wherein, The loading point and the displacement measurement point are at the same cross-section position.

6. The method of claim 5, wherein the method further comprises: The loading point and the displacement measurement point are at different cross-section positions.

7. The method of claim 5, wherein the method further comprises: The method is suitable for load capacity evaluation of the uniform damage of the tensile reinforcement in the reinforced concrete beam.

8. The method of claim 1, wherein, ​

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