A method for predicting the shear strength of rectangular and circular reinforced concrete columns

Abstract

The present invention provides a method for predicting the shear strength of rectangular and circular reinforced concrete columns, comprising: S1: selecting a calibration dataset and a validation dataset; S2: constructing a shear strength polynomial model; S3: selecting the optimal model; S4: verifying the accuracy of the polynomial model predictions based on the validation dataset; and S5: outputting the prediction model. The present invention can produce a highly accurate shear strength prediction model applicable to columns with rectangular and circular cross-sections. The prediction model is unaffected by the failure morphology of reinforced concrete columns, eliminates the need for material and dimensional constraints, and has a wide range of applicability. During the application of big data, the shear strength prediction formula can be updated promptly to ensure prediction accuracy. The method also excels in data fusion and possesses strong adaptability.

Description

Technical Field

[0001] The present invention relates to a method for predicting the shear strength of rectangular and circular reinforced concrete columns. Background Art

[0002] Predicting the shear strength of structural elements under gravity loads and ground motions is an essential component of seismic design. Among all major structural components, the crucial role of columns in load transfer and redistribution, structural stability, and collapse prevention is well understood through observations following past earthquakes. Over the past few decades, numerous analytical, numerical, and experimental studies have been conducted to evaluate the shear strength of reinforced concrete columns. However, current empirical and numerical model predictions still suffer from significant discrepancies (i.e., uncertainties) relative to test data. Summary of the Invention

[0003] Purpose of the invention: To solve the technical problems existing in the background technology, the present invention proposes a method for predicting the shear strength of rectangular and circular reinforced concrete columns, comprising the following steps:

[0004] Step 1: Select the existing rectangular and circular reinforced concrete column shear test results as the calibration dataset and validation dataset;

[0005] Step 2: According to the factors affecting shear strength, the geometric parameters and constitutive parameters of the column are selected and a shear strength polynomial model is constructed;

[0006] Step 3: Based on the selected calibration data set, perform a significance test on the shear strength polynomial model parameters, and select the model parameters involved in the fitting based on the test results.

[0007] Step 4: Perform regression analysis on the selected model parameters and select the optimal model coefficients;

[0008] Step 5: Based on the validation dataset and the Monte Carlo method, an exhaustive search is performed in the polynomial model space to ensure the accuracy and optimal solution of the shear strength polynomial model prediction. The existing experimental database is randomly divided into a calibration set and a validation set. Through regression analysis of the calibration set data, a polynomial equation for the ultimate shear bearing capacity of rectangular columns is established. The prediction model is verified using the validation dataset to obtain a data-driven model of shear strength.

[0009] Step 6: Output the shear strength prediction formula.

[0010] Furthermore, step 1 includes: existing published shear test results of rectangular and circular reinforced concrete columns can be used as the content of the data set, the sample of the data set is no less than 100 specimens, 70% of the selected samples are randomly selected as the calibration data set, and 30% are randomly selected as the verification data set.

[0011] Furthermore, step 2 includes: the factors affecting the shear strength polynomial model include the aspect ratio of the column, the axial compression ratio, stirrups, and longitudinal reinforcement, and the specific variables include the concrete compressive strength f′ c , the total cross-sectional area of ​​the column A g ; Area of ​​stirrups A st , yield strength f yt ; Area of ​​longitudinal reinforcement A sl , yield strength f yl Column section height h; c is the neutral axis height; a is the distance from the maximum bending moment section to the inflection point; axial load P; effective width b and effective depth d of the column section; stirrup reinforcement ratio ρ t , longitudinal reinforcement ratio ρ l .

[0012] Furthermore, the specific variables are not constrained by the column failure morphology, and there is no need to limit the parameter value range. Generally, the value range of a / d is 2 to 4, and f′ c The value range is 13~45MPa, f yt 、f yl The value range is 300~650MPa, ρ l The value range is 0.01~0.04, ρ t f yt / f′ c The value range is 0.01 to 0.12.

[0013] Furthermore, step 2 includes: the influencing factors of the shear strength polynomial model are expressed as 7 main model parameters, X1 and X5 represent the influence of axial load on the shear strength of the column, X5=(hc)P / 2a; X2 represents the effect of column aspect ratio on shear strength, X3 and X6 represent the influence of stirrups on shear strength, X3= st f yt d / s, s represents the stirrup spacing; X4 and X7 represent the effect of longitudinal reinforcement on shear strength, X4= sl f yl ,

[0014] Furthermore, step 2 includes: the shear strength polynomial model is fitted using polynomials, which are linear, mixed and second-order combinations of parameters X1,...,X7, expressed as Among them, α0, α i , α ij , α ii is the regression coefficient, i≠j.

[0015] Furthermore, step 3 includes: based on the selected calibration data set, using SPSS 25 software package to max Perform polynomial regression analysis and remove model parameters X with negative regression coefficients i The significance factor Sig was used to evaluate the influence of model parameters on shear strength, and model parameters with Sig>0.05 were removed; for the three groups of parameters X1 and X5, X3 and X6, and X4 and X7, the model parameters with smaller significance (smaller is the smaller one in each group) were eliminated respectively to determine the final fitting model parameters.

[0016] Step 4 includes: calculating the model regression coefficients α0, α i , α ij , α ii and the correlation coefficient R 2 .

[0017] Step 4 also includes: for the regression coefficient combination, select R 2 The set of regression coefficients with the largest value and V1 closest to 1 is taken as the optimal model coefficients, and V1 represents the ratio of the predicted value of the shear strength polynomial model to the actual measured value.

[0018] Step 5 includes: randomly selecting some data in the validation data set for regression analysis, and recording the fitting results that meet the significance and the fitting parameters are positive; randomly taking N1 values ​​(for example, 100) in the validation data set, repeating the regression process, and obtaining the maximum correlation coefficient, which is compared with the correlation coefficient R in step 4. 2 By comparison, if both are greater than 0.95, the model is reliable. Otherwise, the parameter screening and fitting in step 3 need to be repeated.

[0019] The method of the present invention can be applied to the prediction of the shear strength of circular reinforced concrete columns.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) A high-precision shear strength prediction model can be obtained;

[0022] (2) This shear strength prediction method is applicable to rectangular and circular cross-section columns, covering the cross-sectional shapes of most reinforced concrete columns;

[0023] (3) The prediction model is not affected by the failure mode of reinforced concrete columns and does not require material and size constraints, making it widely applicable.

[0024] (4) In the application process of big data, the shear strength prediction formula can be updated in a timely manner to ensure the prediction accuracy;

[0025] (5) It is good at data fusion and has strong adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more apparent.

[0027] Figure 1 Flow chart of the method of the present invention.

[0028] Figure 2 It is a schematic diagram of the predicted shear strength and the measured shear strength using the present invention. DETAILED DESCRIPTION

[0029] Example

[0030] See Figure 1 The present invention provides a technical solution, a data-driven model for predicting the shear strength of rectangular and circular reinforced concrete columns, comprising the following steps:

[0031] 1. 100 reinforced concrete column shear strength values ​​were selected from existing literature as a database for strength prediction, 70 of which were randomly selected as calibration data sets and 30 as validation data sets.

[0032] 2. The main data range of rectangular columns is shown in Table 1 below.

[0033] Table 1

[0034]

[0035]

[0036] 3. Apply the above data to perform polynomial The regression analysis was performed using SPSS 25 software package. The analysis process was as follows: Figure 1 shown.

[0037] 4. In order to more intuitively analyze the impact of each polynomial term on the intensity prediction results, regression analysis of linear terms only, linear terms and mixed terms, and linear terms and second-order terms were performed respectively. The significance test sig X1 = 0.026, sig X5 = 0.000, sig X4 = sig X7, sig X6 = 0.626. After eliminating parameters X1, X6, and X7, the obtained regression coefficients and correlation coefficients are shown in Table 2.

[0038] Table 2

[0039]

[0040]

[0041] 5. The fitting results of the second-order term and the mixed term have very little effect on the change of the correlation coefficient, and the contribution of the second-order term and the mixed term to the predicted value is very small, so the optimal fitting result is selected as the linear fit.

[0042] 6. Take a set of reinforced concrete columns for testing, f′ c =28.7MPa, A st =243mm 2 , f yt =469MPa, sl =5158mm 2 , f yl =436MPa, h=457.2mm, c=452.3mm, a=1453.2mm, P=667.2kN, b=457.2mm, d=365.1mm, s=274.3mm. The model parameters were calculated using the geometric mechanical parameters of the selected column and substituted into the linear fitting polynomial. The shear strength provided by each model parameter was calculated to be: α2X2=98.8kN, α3X3=25.8kN, α4X4=83.2kN, α5X5=61.8kN, α0=15kN. The maximum calculated shear strength of the column is consistent with the measured shear strength (the predicted value is 284.6kN, and the experimental value is 294.5kN). The calculation results of other data in the validation set are as follows. Figure 2 shown.

[0043] The present invention provides a method for predicting the shear strength of rectangular and circular reinforced concrete columns. While there are numerous methods and approaches for implementing this technical solution, the foregoing description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the present invention. Any components not specified in this embodiment may be implemented using existing technologies.

Claims

1. A method for predicting the shear strength of rectangular and circular reinforced concrete columns, characterized in that The steps include: Step 1: Select the existing rectangular and circular reinforced concrete column shear test results as the calibration dataset and validation dataset; Step 2: According to the factors affecting shear strength, the geometric parameters and constitutive parameters of the column are selected and a shear strength polynomial model is constructed; Step 3: Based on the selected calibration data set, perform a significance test on the shear strength polynomial model parameters, and select the model parameters involved in the fitting based on the test results; Step 4: Perform regression analysis on the selected model parameters and select the optimal model coefficients; Step 5: Based on the validation dataset and Monte Carlo method, perform an exhaustive search in the polynomial model space; Step 6: Output the shear strength prediction formula; Step 2 includes: the factors affecting the shear strength polynomial model include the aspect ratio of the column, the axial compression ratio, stirrups, and longitudinal reinforcement. The specific variables include the concrete compressive strength f′ c , the total cross-sectional area of ​​the column A g ; Area of ​​stirrups A st , yield strength f yt ; Area of ​​longitudinal reinforcement A sl , yield strength f yl Column section height h; c is the neutral axis height; a is the distance from the maximum bending moment section to the inflection point; axial load P; effective width b and effective depth d of the column section; stirrup reinforcement ratio ρ t , longitudinal reinforcement ratio ρ l ; The specific variables are not constrained by the column failure morphology, and there is no need to limit the parameter value range; Step 2 includes: the influencing factors of the shear strength polynomial model are expressed as 7 main model parameters, X1 and X5 represent the influence of axial load on the shear strength of the column, X5=(hc)P / 2a; X2 represents the effect of column aspect ratio on shear strength, X3 and X6 represent the influence of stirrups on shear strength, X3 = A st f yt d / x, s represents the stirrup spacing; X4 and X7 represent the effect of longitudinal reinforcement on shear strength, X4 = A sl f yl , Step 2 includes: the shear strength polynomial model is fitted using polynomials, which are linear, mixed and second-order combinations of parameters X1,...,X7, expressed as shear strength Among them, α0, α i , α ij , α ii is the regression coefficient, i≠j; Step 3 includes: based on the selected calibration data set, max Perform polynomial regression analysis and remove model parameters X with negative regression coefficients i The significance factor Sig was used to evaluate the effect of model parameters on shear strength, and model parameters with Sig>0.05 were removed. For the three groups of parameters X1 and X5, X3 and X6, and X4 and X7, the model parameters with smaller significance in each group were removed to determine the final fitting model parameters. Step 4 includes: calculating the model regression coefficients α0, α i , α ij , α ii and the correlation coefficient R 2 ; Step 4 also includes: for the regression coefficient combination, select R 2 The set of regression coefficients with the largest value and V1 closest to 1 is taken as the optimal model coefficients, and V1 represents the ratio of the predicted value of the shear strength polynomial model to the actual measured value; Step 5 includes: randomly selecting some data in the validation data set for regression analysis, and recording the fitting results that meet the significance and the fitting parameters are positive; randomly taking values ​​N1 times in the validation data set, repeating the regression process, and obtaining the maximum correlation coefficient, which is compared with the correlation coefficient R in step 4. 2 By comparison, if both are greater than 0.95, the model is reliable. Otherwise, the parameter screening and fitting in step 3 need to be repeated.

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