CN113505513B - Calculation method for stress concentration coefficient of rusted suspender - Google Patents
Calculation method for stress concentration coefficient of rusted suspender Download PDFInfo
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Abstract
The invention discloses a calculation method of a stress concentration coefficient of a rusted suspender, which considers the radius r of a rusted pit on the suspender, the depth D of the rusted pit and a functional relation between the diameter D of the suspender and the stress concentration coefficient K of the rusted suspender, obtains a plurality of groups of stress concentration data by establishing a model and calculating based on the model, fits the data and further obtains an expression of the stress concentration coefficient K of the rusted suspender. The expression can replace a finite element method to obtain the stress concentration coefficient of the corroded ball pit suspender, simplifies the calculation of the stress concentration coefficient of the corroded ball pit suspender, provides a quick method for the stress concentration coefficient of the corroded ball pit suspender in subsequent engineering, avoids the problem that the calculation by the finite element method is time-consuming and complicated, and saves time cost.
Description
Technical Field
The invention relates to the field of corrosion of bridge suspenders, in particular to a calculation method for a stress concentration coefficient of a corroded suspender.
Background
The suspender plays an important role in various bridges as a key component of the bridge, and is an important stressed component in a tied arch bridge and a suspension bridge, so that the safety of the suspender is concerned with the safety of the whole bridge. However, as the service time increases, the hanger rod is often corroded under the combined action of the external environment and the fatigue load, and the corrosion weakens the section of the hanger rod, so that the fatigue performance of the hanger rod is reduced, the fatigue life is shortened, and the safety of the hanger rod is seriously threatened. Therefore, in order to better judge the danger degree of the corrosion to the weakening of the cross section of the suspender, the stress concentration coefficient is introduced as an important index for judging the safety of the corrosion suspender structure. However, the traditional calculation of the stress concentration coefficient is mostly determined by theoretical gradual derivation or experiment by using a finite element method, which is too time-consuming and complex to be beneficial to the subsequent research on the corrosion of the bridge hanger rod. Therefore, it is necessary to provide a method for rapidly calculating the stress concentration coefficient of the rusty suspender.
Disclosure of Invention
In view of the foregoing, there is a need to provide a method for calculating a stress concentration coefficient of a rusty boom, so as to quickly and accurately calculate the stress concentration coefficient of the rusty boom, and the method has strong applicability.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a calculation method of a stress concentration coefficient of a corrosion suspender considers a functional relation between the radius r of a corrosion pit on the suspender, the depth D of the corrosion pit and the diameter D of the suspender and the stress concentration coefficient K of the corrosion suspender, and the expression of the stress concentration coefficient K of the corrosion suspender is as follows:
further, the depth d of the rust pit ranges from 0< d <2 r.
For the above corrosion suspender stress concentration coefficient K expression, it is obtained by the following method: firstly, establishing a plurality of groups of corrosion suspender finite element models with different corrosion pit radiuses r, corrosion pit depths D and suspender diameters D by using an ANSYS (ANSYS) based on a finite element method; then, according to the existing research on the V-shaped groove of the rod, establishing the same V-shaped groove model by using ANSYS, calculating a stress concentration coefficient K, comparing the stress concentration coefficient K with the existing research data, verifying the reliability of the established ANSYS corrosion suspender model, and solving the corresponding stress concentration coefficient by using the established finite element model after verifying the reliability of the established model; and finally, fitting a functional relation among the radius r of the corrosion pit, the depth D of the corrosion pit, the diameter D of the suspender and the stress concentration coefficient K of the corrosion suspender according to a plurality of groups of data to obtain an expression of the stress concentration coefficient K of the corrosion suspender.
Therefore, compared with the prior art, the invention has the following beneficial effects:
1. aiming at the problem that the stress concentration coefficient of the existing corrosion suspender is difficult to obtain quickly and simply, the invention provides a functional relation formula, and the required stress concentration coefficient can be quickly calculated by simply measuring the diameter of the suspender, the radius of a corrosion pit and the depth. The formula can replace a finite element method to obtain the stress concentration coefficient of the corroded ball pit suspender, simplify the calculation of the stress concentration coefficient of the corroded ball pit suspender, provide a quick method for the stress concentration coefficient of the corroded ball pit suspender in subsequent engineering, avoid the problem that the calculation by the finite element method is time-consuming and complicated, and save time and cost.
2. The method is suitable for calculating the stress concentration coefficients of various rusted ball pit suspenders, and has the advantages of simple structure calculation, convenience in operation and high popularization value.
Drawings
FIG. 1 is a model of a ball pit rusted boom, with an overall mesh division and a partially enlarged view of a rusted pit;
FIG. 2 is a rod model of the same V-shaped groove as in the prior study, created using ANSYS;
FIG. 3 is a mesh division diagram of the created V-shaped groove rod model;
FIG. 4 is a plot of the fitted stress concentration versus the ANSYS finite element calculated stress concentration.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Firstly, establishing a corrosion suspender model
1. Selecting the shape of the model rust pit: it has been studied to classify the shape of a steel bar corrosion pit into an open type and a deep and narrow type by observing the shape of the corrosion pit. Wherein, the shape of the open type corrosion pit is divided into a spherical crown type, a hemisphere and the like, so the corrosion pit can be simplified into a sphere-like corrosion pit. Another deep and narrow type corrosion pit shape includes a cone shape, a frustum shape, etc., and researchers (such as Pidaparti, etc.) have found that the cone-shaped corrosion pit gradually changes into a hemispherical corrosion pit with the increase of corrosion time. Therefore, according to the conclusion of the research, the hanger rod with the spherical rust pit is selected and established for experimental simulation.
2. A boom model with spherical rust was created with ANSYS: the model selects structural steel as a material, and the material characteristics are set, specifically, the density is 7800kg/m3Young's modulus of 3X 1011The Poisson's ratio was 0.3. The height of the suspender model is 12mm, the diameter of the suspender is D, and the center of the surface of the suspender is provided with a corrosion ball pit with the radius of r and the depth of D.
3. Grid division: and cutting the model, and cutting the model at the positions of 1mm above, below, left and right of the edge of the sphere of the hemispherical pit, wherein the whole part except the sphere pit part is divided by 0.2mm per unit in a sweeping way, and the sphere pit part is divided by 0.06mm per unit in a hexahedron way.
The above model and meshing are shown in fig. 1.
Secondly, verifying the reliability of the model
To ensure the reliability of the model, the calculation of the stress concentration coefficient of the V-shaped groove of the bar in the low-stress blanking [ J ] is based on the existing research on the V-shaped groove of the bar (Zhang Li Jun, Zhang De Bao, Zhou Tree En, Wang Xiao Qiang, Wang Han Xiang, Zhao Sheng ton, Liu Yong hong, Linjing school)]The plastic engineering journal (2018) 254-
60 degrees are taken, the depth q is taken as 1mm, the diameter of the rod model is taken as 15mm, the length of the rod is 40mm, and the V-shaped groove is positioned at the position of 5mm at the left end of the rod. Keeping the parameters unchanged, changing the radius rho of the bottom arc, and solving the stress concentration coefficient K. Grid division: the two sides of the V-shaped groove are divided at a position 1mm away from the center of the V-shaped groove, the rod model is divided into three parts, wherein the V-shaped groove part is mapped and divided in 0.3mm per unit, and the other two parts are swept and divided in 0.6mm per unit, as shown in figure 3. Operating the model and calculating to obtain the stress concentration coefficient K1The obtained stress concentration coefficient K1And the actual stress concentration coefficient K obtained by the test in the prior research2For comparison, the results are shown in Table 1 below.
TABLE 1
| ρ(mm) | K1 | K2 | Error of the measurement |
| 0.2 | 2.657 | 2.62 | 1.41％ |
| 0.3 | 2.252 | 2.27 | 0.799％ |
| 0.4 | 2.074 | 2.09 | 0.77％ |
| 0.5 | 1.829 | 1.81 | 1.05％ |
As can be seen from Table 1, the stress concentration coefficient K calculated by ANSYS in the present application1Within the tolerance of 8.4% allowed by the above-mentioned prior studies, the model established by the present invention can be considered to be basically consistent, i.e. the rusting model established by the present invention using ANSYS is proved to be reliable.
And thirdly, fitting a functional relation among the radius r of the corrosion pit, the depth D of the corrosion pit, the diameter D of the suspender and the stress concentration coefficient K of the corrosion suspender.
Selecting a plurality of groups of rusted ball pits and hanging rods with different sizes, and calculating the corresponding stress concentration coefficient by using the established finite element model, which is specifically shown in the following table 2.
TABLE 2 stress concentration coefficients corresponding to the sizes of multiple groups of rusty ball pits and the sizes of suspenders
Based on the correlation study (mavialong; study on mechanical properties of uneven corrosion paired arch bridge hanger bar [ D ]; Chongqing traffic university; 2016), it was found that the stress concentration coefficient and the size of the corrosion pit, and the stress concentration coefficient and the size of the hanger bar have a mutual relationship between each other, and therefore, the stress concentration coefficient can be represented by the size of the corrosion pit and the size of the hanger bar. Then, according to the data in table 2 above, the formula K fitted with 1stOpt is (r, D) as follows:
in summary, the calculation method of the stress concentration coefficient of the corrosion suspender provided by the invention considers the radius r of the corrosion pit on the suspender, the depth D of the corrosion pit and a functional relation between the diameter D of the suspender and the stress concentration coefficient K of the corrosion suspender, so as to obtain the stress concentration coefficient K expression of the corrosion suspender as follows:
the depth d of the rust pit is set in a range of 0< d <2 r.
In addition, in order to verify the calculation accuracy of the corrosion suspender stress concentration coefficient K expression provided by the invention, the corrosion suspender stress concentration coefficient K value obtained by solving through a finite element method and the corrosion suspender stress concentration coefficient K' value obtained by calculating through the expression provided by the invention are compared and analyzed, the comparison data is shown as a table 3, and the data in the table 3 is drawn into a broken line diagram, particularly shown as a table 4.
TABLE 3 comparison data of stress concentration coefficient calculated by the present invention and that calculated by ANSYS finite element
Based on the above table 3, it can be seen that the value of the stress concentration coefficient K of the corrosion boom calculated by the finite element method and the value of the stress concentration coefficient K' of the corrosion boom calculated by the expression given by the present invention are very close, the error is 4.01% at the maximum, and within the allowable error range of the research, the expression of the stress concentration coefficient K of the corrosion boom given by the present invention is considered to be accurate, and the present invention can be applied to practical engineering.
The above description is intended to describe in detail the preferred embodiments of the present invention, but the embodiments are not intended to limit the scope of the claims of the present invention, and all equivalent changes and modifications made within the technical spirit of the present invention should fall within the scope of the claims of the present invention.
Claims (2)
1. A calculation method of the stress concentration coefficient of a corrosion suspender is characterized by comprising the following steps: considering the radius r of a corrosion pit on the suspender, the depth D of the corrosion pit and a functional relation between the diameter D of the suspender and the stress concentration coefficient K of the corrosion suspender, the expression of the stress concentration coefficient K of the corrosion suspender is as follows:
2. the method for calculating the stress concentration coefficient of the rusty suspender as claimed in claim 1, wherein: the depth d of the corrosion pit ranges from 0< d <2 r.
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