A method for calculating stress concentration coefficient of suspender under internal steel wire corrosion state

Abstract

The application discloses a method for calculating a stress concentration coefficient of a suspender under an internal steel wire corrosion state, which considers a functional relationship between a radius r of a corrosion pit on an edge steel wire in a steel wire bundle in the suspender, a depth d of the corrosion pit, a steel wire diameter D, a number n of steel wires in the steel wire bundle and a corrosion suspender stress concentration coefficient K, and through establishment of a finite element model and calculation by using a finite element method, a plurality of groups of data obtained by calculation are fitted to obtain an expression of the corrosion suspender stress concentration coefficient K, which considers an influence of the remaining non-corrosion steel wires in the steel wire bundle in the suspender on the overall stress concentration coefficient of the suspender, and the expression can improve the calculation precision of the stress concentration coefficient, in addition, through the obtained expression, the stress concentration coefficient of the suspender under the internal steel wire corrosion state can be quickly calculated through simple measurement of n, D, r and d, and therefore the application can provide a quick method for calculating the stress concentration coefficient of the suspender in subsequent engineering, and the calculation is accurate and efficient.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of bridge suspender corrosion, and in particular to a method for calculating the stress concentration factor of a suspender under the condition of internal steel wire corrosion. BACKGROUND

[0002] The suspender is an important force transmission component in the bridge structure, and is usually composed of parallel steel wire bundles. As the service time increases, the steel wires in the suspender are prone to corrosion damage at the anchoring end and other areas due to the double influence of external environmental corrosion and fatigue load. The corrosion damage causes stress concentration, which reduces the service life of the suspender, and thus causes many suspender to suddenly break at a much lower expected service life.

[0003] Considering that the stress amplification factor at the stress concentration position can be represented by the stress concentration factor, it is necessary to derive the stress concentration factor of the suspender under the condition of internal steel wire corrosion in order to better judge the risk level of the suspender under the condition of internal steel wire corrosion. The traditional calculation of the stress concentration factor mostly uses finite element method and test method, which is complex and time-consuming, and is not conducive to simplifying the calculation and popularization. The patent CN113505513B proposes a method for calculating the stress concentration factor of a corroded suspender. Although the expression given by this calculation method can replace the finite element method to obtain the stress concentration factor of a suspender with a corrosion pit, it simplifies the calculation of the stress concentration factor of a suspender with a corrosion pit, provides a quick method for the stress concentration factor of a suspender with a corrosion pit in engineering, avoids the time-consuming and complex problem of using finite element method, and saves time and cost. However, this calculation method only studies a single corroded steel wire in the suspender, and does not consider the influence of the remaining non-corroded steel wires in the steel wire bundle on the suspender, so the calculation result is not accurate enough.

[0004] Therefore, it is necessary to provide a method for calculating the stress concentration factor of a suspender under the condition of internal steel wire corrosion considering the influence of the steel wire bundle. SUMMARY

[0005] In view of the above, it is necessary to provide a method for calculating the stress concentration factor of a suspender under the condition of internal steel wire corrosion, which considers the influence of the remaining non-corroded steel wires in the steel wire bundle on the overall stress concentration factor of the suspender. The expression obtained by this calculation method can realize fast and accurate calculation of the stress concentration factor of a corroded suspender, and the calculation result is more accurate and has strong applicability.

[0006] To achieve the above purpose, the technical solution adopted by the present application is:

[0007] A method for calculating a stress concentration coefficient of a boom in an internal steel wire corrosion state, considering a functional relationship between a radius r of a corrosion pit on an edge steel wire in a steel wire bundle in the boom, a depth d of the corrosion pit, a steel wire diameter D, a number n of steel wires in the steel wire bundle, and a corrosion boom stress concentration coefficient K, and the expression of the corrosion boom stress concentration coefficient K is:

[0008]

[0009] Further, the radius r of the corrosion pit ranges from 0 to 2r.

[0010] Further, the depth d of the corrosion pit ranges from 0 to 2r.

[0011] For the expression of the corrosion boom stress concentration coefficient K, the present application is established by the following method:

[0012] First, orthogonal design method is used to perform orthogonal design on the four parameters of the radius r of the corrosion pit, the depth d of the corrosion pit, the steel wire diameter D, and the number n of steel wires in the steel wire bundle.

[0013] Second, ANSYS finite element software is used to establish a finite element model of the boom in the internal steel wire corrosion state with different radius r of the corrosion pit, depth d of the corrosion pit, steel wire diameter D, and number n of steel wires in the steel wire bundle according to the design results, and the corresponding boom stress concentration coefficient is obtained by using the established finite element model.

[0014] Finally, the functional relationship between the radius r of the corrosion pit, the depth d of the corrosion pit, the steel wire diameter D, and the number n of steel wires and the corrosion boom stress concentration coefficient K is fitted according to multiple sets of data, and the correctness of the formula is verified by comparing with the results of ANSYS finite element calculation, so as to obtain the expression of the boom stress concentration coefficient K in the internal steel wire corrosion state.

[0015] Compared with the prior art, the present application has the following beneficial effects:

[0016] 1. The present application aims at the problem of low calculation accuracy of the stress concentration coefficient of the boom in the internal steel wire corrosion state, considers the influence of the remaining non-corrosion steel wires in the steel wire bundle in the boom on the overall stress concentration coefficient of the boom, and thus improves the calculation accuracy of the stress concentration coefficient.

[0017] 2、The present application is directed to the problem that the stress concentration coefficient of the suspender is not high under the internal steel wire corrosion state, a function relationship formula of the suspender stress concentration coefficient K and the corrosion pit radius r, the corrosion pit depth d, the steel wire diameter D and the number of steel wires in the steel wire bundle n is established, the expression of the suspender stress concentration coefficient K is obtained through the function relationship formula, in this way, the suspender stress concentration coefficient under the internal steel wire corrosion state can be quickly calculated through simple measurement of n, D, r and d, which provides a quick method for the calculation of the suspender stress concentration coefficient in subsequent engineering.

[0018] 3、The present application is simple to calculate, convenient to operate, strong in applicability and has high popularization value. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 is the steel wire distribution diagram in the embodiment of the present application.

[0020] Figure 2 is the suspender finite element model under the internal steel wire corrosion state in the embodiment of the present application. DETAILED DESCRIPTION

[0021] The present application will be further described below in combination with the drawings and embodiments.

[0022] I. Orthogonal design

[0023] 1. Shape selection of steel wire surface corrosion pit: existing researches observe the shape of steel bar corrosion pit and summarize the shape of corrosion pit into open type and deep narrow type. Among them, the open type corrosion pit shape includes spherical cap type, hemispherical type and the like, so this kind of corrosion pit can be simplified as a spherical corrosion pit. Another deep narrow type corrosion pit shape includes conical type, frustum type and the like, and relevant researches find that the conical corrosion pit will gradually become a hemispherical corrosion pit with the increase of corrosion time. Therefore, according to the above research conclusion, the present application selects to establish a spherical corrosion pit for simulation.

[0024] 2. Orthogonal design: the test parameters include the radius r of the corrosion pit, the depth d of the corrosion pit, the steel wire diameter D and the number of steel wires n in the steel wire bundle. In this embodiment, the radius r of the corrosion pit is 0.1mm, 0.5mm and 1.0mm; the radius d of the corrosion pit is 0.1mm, 0.5mm and 1.0mm; the steel wire diameter D is 5mm, 6mm and 7mm; and the number of steel wires n in the steel wire bundle is 61, 91 and 127. It is worth noting that the above parameter values can be any value within the range of 0 d<2r, the embodiment of the present application only takes the above parameter values for illustration, but the values of the parameters are not limited to the specific values given in this embodiment. Orthogonal design software (such as orthogonal design assistant) is used for orthogonal design, and the obtained orthogonal design results are shown in the following table 1.

[0025] Table 1 orthogonal design results

[0026]

[0027]

[0028] II. Establishing finite element model of the boom under the internal steel wire corrosion state

[0029] The model selects structural steel as the material, and sets the material properties, i.e. the density is 7850 kg / m 3 , the Young's modulus is 2*10 11 Pa, and the Poisson's ratio is 0.3. The height of the steel wire in the boom is 24 mm, the diameter of the steel wire is D, the surface center of the outermost steel wire has a corrosion pit with a radius of r and a depth of d, the number of the steel wires in the steel wire bundle is n, and the sectional view of the steel wire in the boom under different steel wire numbers is shown in the following Figure 1 The finite element model of the boom under the specific internal steel wire corrosion state is shown in the following Figure 2 .

[0030] Constraints and loads of the model: the top of the steel wire is fixed, a circular rigid flat plate is established at the bottom and connected with all the steel wires, the contact is set to be non-separation, and a vertical uniform distributed tension is applied to the flat plate, so as to realize the internal force redistribution of the steel wire under different damage conditions.

[0031] As can be seen, the model considers the influence of the remaining non-corrosion steel wires in the steel wire bundle in the boom on the stress concentration coefficient of the whole boom, so that the calculation precision of the stress concentration coefficient can be improved.

[0032] III. Fitting the expression of the stress concentration coefficient K of the boom under the internal steel wire corrosion state.

[0033] The corresponding stress concentration coefficients of the boom under each parameter in table 1 are shown in the following table 2 through finite element calculation of the finite element model.

[0034] Table 2: The corresponding stress concentration coefficients of the boom under each parameter obtained through finite element calculation

[0035]

[0036]

[0037] According to the data in the above table 2, the formula K=f(r,d,D,n) is fitted by 1stOpt as follows:

[0038]

[0039] It is known from 1stOpt that the fitting degree of the formula is 99.12%. It should be noted that the value range of the radius r of the corrosion pit in the above formula is The depth d of the rust pit is in the range of 0 < d < 2r.

[0040] In addition, in order to further verify the accuracy of the formula for calculating the stress concentration coefficient of the suspender under the internal steel wire rust state given by the present application, the present application compares the stress concentration coefficient K obtained by the finite element method with the value of the stress concentration coefficient K1 calculated by the calculation method of the stress concentration coefficient of the suspender under the internal steel wire rust state given by the present application. The comparison data is shown in Table 3.

[0041] Table 3 Comparison data of stress concentration coefficients calculated by the formula of the present application and the finite element method

[0042]

[0043] Based on the above Table 3, the value of the stress concentration coefficient K of the suspender under the internal steel wire rust state calculated by the finite element method and the value of the stress concentration coefficient K1 calculated by the expression given by the present application are very close, with a maximum error of only 6.06%. Within the allowable error range of the study, it can be considered that the calculation method of the stress concentration coefficient of the suspender under the internal steel wire rust state given by the present application is accurate, and it can be applied to actual engineering.

[0044] The above description is a detailed description of the preferred and feasible embodiments of the present application, but the embodiments are not intended to limit the scope of the patent application of the present application. Any equivalent changes or modifications made under the technical spirit of the present application should be considered within the scope of the patent application of the present application.

Claims

1. A method for calculating the stress concentration factor of a boom in the internal steel wire corrosion state, characterized by, Considering the functional relationship between the radius r of the corrosion pit on the edge wire of the steel wire bundle in the boom, the depth d of the corrosion pit, the diameter D of the wire and the number n of the wires in the steel wire bundle and the stress concentration coefficient K of the corroded boom, the expression of the stress concentration coefficient K of the corroded boom is:

2. A method of calculating the stress concentration factor of a boom in the presence of internal steel corrosion according to claim 1, characterized in that, The radius r of the corrosion pits ranges from 3. A method of calculating the stress concentration factor of a boom in the presence of internal steel corrosion according to claim 1, characterized in that, The depth d of the corrosion pit is in the range of 0 < d < 2r.

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