CN118378503A - Calculation method for elastic distortion buckling critical stress of local corrosion cold-formed thin-walled steel column - Google Patents
Calculation method for elastic distortion buckling critical stress of local corrosion cold-formed thin-walled steel column Download PDFInfo
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- 229910000831 Steel Inorganic materials 0.000 title claims abstract description 108
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- 230000007797 corrosion Effects 0.000 title claims abstract description 84
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- 238000004364 calculation method Methods 0.000 title claims abstract description 32
- 230000005489 elastic deformation Effects 0.000 claims abstract description 32
- 238000000034 method Methods 0.000 claims description 77
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- JEIPFZHSYJVQDO-UHFFFAOYSA-N iron(III) oxide Inorganic materials O=[Fe]O[Fe]=O JEIPFZHSYJVQDO-UHFFFAOYSA-N 0.000 claims description 19
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- 238000006073 displacement reaction Methods 0.000 claims description 12
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Abstract
The invention discloses a calculation method of elastic distortion buckling critical stress of a local corrosion cold-formed thin-walled steel column, belonging to the technical field of corrosion environment steel structure durability evaluation, comprising the following steps: s1, obtaining the section parameters of the local corrosion cold-formed thin-walled steel column by equivalent of the uneven thickness of the local corrosion cold-formed thin-walled steel column to uniform thickness; s2, analyzing the stress of the elastic deformation curve Qu Linjie according to a calculation model of the elastic deformation and buckling critical load of the local corrosion cold-formed thin-wall steel column; s3, obtaining a solution equation of the elastic distortion buckling critical load according to the unique condition that the homogeneous equation set has a non-zero solution, wherein the series determinant is zero; s4, correcting half wavelengths corresponding to the horizontal spring stiffness, the rotary spring stiffness and the buckling critical load to obtain the elastic distortion buckling critical load of the rusted cold-formed thin-walled steel column; and S5, calculating the elastic distortion buckling critical stress of the local corrosion cold-formed thin-wall section steel according to the elastic distortion buckling critical load.
Description
Technical Field
The invention relates to the technical field of corrosion environment steel structure durability evaluation, in particular to a calculation method for the elastic distortion buckling critical stress of a local corrosion cold-formed thin-walled steel column.
Background
The cold-formed thin-wall section steel is formed by rolling or hydraulic cold-working steel plates, steel strips or steel sheets with the thickness of less than 6mm, and is widely applied to infrastructure engineering due to the advantages of flexible section shape, high section performance, convenient construction, energy conservation, environmental protection and the like. However, many cold-formed thin-walled steel structural projects have serious corrosion problems when in service in corrosive environments such as high humidity, high chloride ions or sulfate ions.
The cold-formed thin-wall steel structure has small wall thickness and slender members, the instability damage is often the main damage form, and the research on the cold-formed thin-wall steel structure is mainly developed around the stability problem. The method for calculating the stable bearing capacity of the cold-formed thin-wall steel member mainly comprises a direct strength method and an effective width method, and the stable bearing capacity of the cold-formed thin-wall steel member is calculated by the direct strength method or the effective width method, and the critical load of elastic buckling is an important parameter, so that the research on the elastic buckling of the cold-formed thin-wall steel member has important engineering application value. Therefore, scholars at home and abroad develop a great deal of research work on the elastic buckling of the non-rusted cold-formed thin-wall steel pressed component, and more innovative results are obtained. In 2021, the elastic buckling performance of the cold-formed steel spliced pole is researched through compression tests and numerical simulation by Zhou et al, the influence of the number and the spacing of screws (screen) on the critical buckling load and mode of the cold-formed steel spliced pole is analyzed, and finally, a new stability calculation theory of the cold-formed steel spliced pole is provided by utilizing a classical single plate stability theory. 2023 year GATHEESHGAR and the like research the influence of the slenderness ratio of the web, the size of the web hole, the corner radius and the length of the stiffening unit on the elastic shearing buckling performance of the cold-formed steel beam with the web stiffening hole, and consider that the stiffening of the web hole can effectively improve the elastic shearing buckling bearing capacity of the beam. In 2023 Mitsui et al, a simplified formula of buckling coefficients and half wavelength of elastic local buckling critical stress of a cold-formed steel compression member was proposed by using the Timoshenko plate buckling theory and considering plate interaction. The above researches are mainly aimed at the elastic buckling performance of the rusted cold-formed thin-wall steel member, but the elastic buckling performance of the rusted cold-formed thin-wall steel member is rarely reported at present, and particularly, the stress calculation method of the elastic deformation Qu Linjie of the rusted cold-formed thin-wall steel member is adopted.
Disclosure of Invention
The invention aims to provide a method for calculating the elastic distortion buckling critical stress of a local corrosion thin-walled steel column, wherein the formula calculation result is close to the numerical simulation result, and the method can be used for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column.
In order to achieve the purpose, the method for calculating the elastic distortion buckling critical stress of the local corrosion cold-formed thin-walled steel column comprises the following steps:
S1, obtaining the section parameters of the local corrosion cold-formed thin-walled steel column by equivalent of the uneven thickness of the local corrosion cold-formed thin-walled steel column to uniform thickness;
S2, analyzing the stress of the elastic deformation curve Qu Linjie according to a calculation model of the elastic deformation and buckling critical load of the local corrosion cold-formed thin-wall steel column;
s3, obtaining a solution equation of the elastic distortion buckling critical load according to the unique condition that the homogeneous equation set has a non-zero solution, wherein the series determinant is zero;
S4, stiffness of horizontal spring Stiffness of rotary springHalf wavelength corresponding to buckling critical loadCorrecting to obtain the elastic distortion buckling critical load of the rusted cold-formed thin-walled steel column;
And S5, calculating the elastic distortion buckling critical stress of the local corrosion cold-formed thin-wall section steel according to the elastic distortion buckling critical load. Preferably, in step S1, the specific operations are as follows:
the partial rust non-uniform thickness is equivalent to the formula of uniform thickness:
（1）
（2）
（3）
in the method, in the process of the invention, 、AndFor web, flange and bead equivalent thicknesses,、AndFor the thickness of the rust areas of the web, the flange and the curled edge,、AndThe areas of the rust areas of the web plate, the flange and the curled edge are h, b and a, the widths of the web plate, the flange and the curled edge are,The deformation buckling half wavelength of the rustless cold-formed thin-walled steel column is obtained, and t is the original thickness.
The parameters of the section of the local corrosion cold-formed thin-wall steel column are calculated according to the equivalent uniform thickness as follows:
（4）
（5）
（6）
（7）
（8）
（9）
（10）
（11）
in the method, in the process of the invention, The cross section area of the flange-hemming system is rust; is the cross-sectional area of an rustless flange-hemming system; Is a flange-hemming system transverse centroid coordinate; Is the longitudinal centroid coordinate of a flange-hemming system; Is a torsion constant; And Moment of inertia for the cross section to the x-axis and the y-axis; Is the area of the cross-section.
Preferably, in step S2, the specific operations are as follows:
According to the distortion buckling critical load calculation model, respectively establishing a force balance differential equation and a bending moment balance differential equation around the shear center on an x axis and a y axis:
（12）
（13）
（14）
in the method, in the process of the invention, Is the elastic modulus; is the shear modulus; polar moment of inertia for the cross section to the origin of the coordinate; And Is displacement of the shear center along the x-axis and y-axis directions; And Transverse and longitudinal to the cross-sectional shear and cross-sectional centroid; The flange-hemming system is a corner of a shearing mandrel; And Respectively a bending constant and a torsion constant of the section; is a critical load for distortion and buckling; is an elastic support reaction force along the y direction; Is a horizontal spring rate; For rotating the spring rate.
Displacement function of distorted buckling in longitudinal direction:
（15）
（16）
in the method, in the process of the invention, AndIs constant.
The flange-hemming system rotates about the resilient support so that displacement of the shear center in the y-axis direction may be accommodated by the cornerThe method comprises the following steps:
（17）
in the method, in the process of the invention, Is z-direction displacement.
Substituting equation (15), equation (16) and equation (17) into equation (12), equation (13) and equation (14) while canceling according to equation (13) and equation (14)Obtaining an equation set:
（18）
（19）
Due to The only condition that the system of equations is zero is that the coefficients of the system of equations are zero, i.e.:
（20）
（21）
preferably, in step S3, the only condition that the homogeneous equation set has a non-zero solution is that the series determinant is zero, so as to obtain a solution equation of the elastic distortion buckling critical load:
（22）
Wherein, Is the cross-sectional area.
Preferably, in step S4, the horizontal spring rate is adjustedStiffness of rotary springHalf wavelength corresponding to buckling critical loadAnd (3) correcting:
Studies have shown that the web provides a lower horizontal stiffness to the flange-hemming system with little impact on the buckling critical load, and therefore, when calculating the distorted buckling critical load, a horizontal spring rate is assumed 。
The influence of web compressive stress, shearing deformation of a flange-hemming system and corrosion on the stiffness of the rotary spring is considered, and the stiffness of the rotary spring is corrected:
（23）
wherein: For the equivalent stiffness of the web plate, For the equivalent compressive stress of the web plate,Is thatAnd (3) the deformation buckling critical load.
Consider the rust to correct the half wavelength:
（24）
equation (23), equation (24) and Substituting the formula (22) to obtain the distortion buckling critical load of the local corrosion cold-formed thin-walled steel member:
（25）
in the method, in the process of the invention, The deformation buckling critical load of the cold-formed thin-walled steel member is locally rusted;、 and The calculation formula for calculating the parameters for the critical load of the distortion buckling is as follows:
（26）
（27）
（28）
in the method, in the process of the invention, AndIn order to calculate the parameters of the device, ， 。
Preferably, in step S5, the elastic distortion buckling critical stress of the local corrosion cold-formed thin-walled steel is calculated according to the elastic distortion buckling critical load, and the specific operation is as follows:
（29）
in the method, in the process of the invention, Is the elastic distortion buckling critical stress of the cold-formed thin-walled steel with local corrosion.
Therefore, the method for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column is adopted, the formula calculation result is close to the numerical simulation result, and the method can be used for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a finite element model of elastic deformation of a local corrosion cold-formed thin-walled steel column;
FIG. 2 is a schematic view of a rusted region;
FIG. 3 is a graph showing the relationship between the elastic deformation buckling critical stress and the volume loss rate of the cold-formed thin-walled steel column at different rusted parts;
FIG. 4 is a graph showing the variation of the elastic deformation buckling critical stress of cold-formed thin-walled steel columns with different rust area sizes; wherein (a) in fig. 4 is the relationship between the elastic distortion buckling critical stress of the rusted cold-formed thin-walled steel column and the width of the rusted region; FIG. 4 (b) is a graph showing the relationship between the elastic deformation buckling critical stress of a rusted cold-formed thin-walled steel column and the length of a rusted region;
FIG. 5 is a graph showing the distortion buckling deformation characteristics of a rusted cold-formed thin-walled steel column; wherein (a) in fig. 5 is a deformation mode of deformation of the rusted cold-formed thin-walled steel column; fig. 5 (b) is a deformed characteristic of a deformed buckling section of a rusted cold-formed thin-walled steel column;
FIG. 6 is a calculation model of the elastic distortion buckling critical stress of a rusted cold-formed thin-walled steel column;
FIG. 7 is a comparison of the calculation result of the elastic distortion buckling critical stress of the rusted cold-formed thin-walled steel column with the result of the finite element; wherein (a) in fig. 7 is web tarnish; fig. 7 (b) shows flange rust; fig. 7 (c) shows the rust of the curl.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs.
Example 1
The invention adopts a finite element characteristic buckling analysis method to study the influence of the size of a rusted part and a rusted area on the buckling performance of cold-formed thin-wall elastic deformation, and comprises the following specific steps:
1 numerical analysis
1.1 Finite element model
The numerical analysis method of the elastic deformation curve Qu Changyong of the cold-formed thin-walled steel column comprises a finite strip method, a generalized beam method and a finite element method, wherein the two methods are relatively simple and mature software exists, but the method is not applicable to components with irregular surfaces at present, so that the method adopts finite elements to analyze the elastic deformation curve performance of the cold-formed thin-walled steel column with local corrosion. The unit selects 8-node thin shell units (S8R 5), and the calculation result of the grid size of 4X 4mm (length X width) is found to be reasonable through convergence analysis. Two ends of the test piece are respectively provided with a node, and the end nodes of the test piece are bound with the nodes and are used for applying load and boundary conditions. The nodes at the two ends of the test piece restrict the degrees of freedom in the x and y directions, rotation restriction is not applied, the middle part of the test piece is applied with z-direction restriction, concentrated load is applied to the nodes at the two ends of the test piece, and specific boundary conditions and loads are shown in figure 1. The invention mainly aims at the elastic buckling performance of the steel column and is buckling mode in a complete elastic state, so that the material parameters required in numerical simulation analysis only have elastic modulus and poisson ratio.
The present invention assumes that the localized rusted region is a regular rectangle and the degree of rusting is expressed by varying the thickness, width and length of the rusted region, as shown in fig. 2. Through finite element analysis, two sections (section A and section B) of test pieces are selected for analysis, wherein the width, thickness and length of a section A of test piece web plate, a flange, a curled edge are respectively 100mm, 70mm, 10mm, 2mm and 1200mm, and the width, thickness and length of a section B of test piece web plate, a flange, a curled edge are respectively 120mm, 80mm, 10mm, 2mm and 1400mm.
1.2 Parameter analysis
1.2.1 Effect of rusted parts
The invention mainly researches the influence of corrosion of a web plate, a flange and a curled edge on the elastic deformation buckling performance of the cold-formed thin-walled steel column, and the corrosion area is positioned in the middle of a test piece, as shown in figure 2. Fig. 3 shows the numerical simulation results of the elastic deformation buckling of the web, flange and hemming rusting cold-formed thin-walled steel column, wherein,Representing the rate of volume loss; And Respectively representing the stress of the elastic deformation curve Qu Linjie of the rusted and non-rusted steel column; AF. AY and AJ respectively represent a web, a flange and a hemming rust A section test piece; BF. BY and BJ respectively represent a web, a flange and a hemming rust B section test piece. As can be seen from table 1 and fig. 3, as the volume loss rate increases, the elastic deformation buckling critical stress of the steel column at different rusted parts is reduced to different degrees, and the reduction rate tends to increase. Meanwhile, the steel column elastic deformation buckling critical stress reduction rate of the hemming corrosion is found to be the largest, the web is corroded, the flange is corroded to be the smallest, and the hemming corrosion has the largest influence on the stress of the cold-formed thin-wall steel column elastic deformation buckling Qu Linjie and the flange is corroded to be the smallest. The edge curl corrosion reduces the width-to-thickness ratio of the plate, so that the edge curl rigidity is reduced, the stiffening effect of the edge curl on the flange is reduced, the critical stress of the web is larger than that of the flange and the edge curl, the torsional buckling constraint of the flange can be provided, the web corrosion reduces the constraint of the web on the flange, and the distortion buckling mainly depends on whether the web and the edge curl provide enough stiffening effect on the flange, so that the stress influence of the edge curl and the web corrosion on the elastic deformation buckling Qu Linjie is larger, the rigidity of the flange is only changed by the edge curl, the constraint of the web and the edge curl on the flange is not changed, and the stress influence of the distortion buckling Qu Linjie is smaller.
1.2.2 Influence of the size of the rusted region
FIG. 4 shows simulation results of the elastic deformation buckling performance of cold-formed thin-walled steel columns with different sizes of rusted areas, wherein the rusted areas are positioned in the middle of a test piece, and c and d represent the width and the length of the rusted areas. As can be seen from (a) in fig. 4, for the a-section web corrosion test piece, the test piece elastic deformation buckling critical stresses of the corrosion area widths of 30mm, 40mm, 50mm and 60mm are respectively reduced by 6.9%, 8.4%, 9.6% and 10.9%, which shows that as the corrosion area width increases, the elastic deformation buckling critical stress is reduced, mainly because the web area width increases to reduce the web-to-flange constraint. The test piece that compares web and edge of a wing corrosion can find, along with corrosion area width increase, the test piece elastic deformation buckling critical stress decline rate of web corrosion is obviously greater than the test piece of edge of a wing corrosion, and the main reason is that the influence of web corrosion to elastic deformation buckling is greater than edge of a wing corrosion, in addition, corrosion area width increase, has increased the plate width to thickness ratio bigger, probably tends to produce local buckling, and the web width is bigger, receives local buckling influence bigger. As can be seen from fig. 4 (b), as the length of the rusted region increases, the elastic deformation buckling critical stress of the test piece gradually decreases, and after the rusted region reaches a certain value, the test piece slowly decreases, and then the test piece gradually decreases, and the decreasing rate has a decreasing trend. According to analysis of the bending mode of the rusted cold-formed thin-walled steel, for the test piece with the section A, the bending half-wave length is about 380mm, the length of the rusted area when the elastic distortion bending critical stress is slowly reduced is about 380mm, and for the test piece with the section B, a similar rule is also provided, and the analysis reasons are probably that when the length of the rusted area is smaller (the length of the rusted area is smaller than the bending half-wave length), the influence of the rusted area on the elastic distortion bending critical stress is large in the main deformation (half-wave length) of the test piece distortion bending, when the length of the rusted area is close to the bending half-wave length, the deformation of the abnormal distortion bending deformation is smaller at the position, the influence of the rusted on the elastic distortion bending critical stress is reduced, and as the length of the rusted area is continuously increased, the influence of the rusted area on the elastic distortion bending critical stress is increased in the main deformation (the other half-wave length). The test piece of comparison web, edge of a wing and turn-up corrosion can find that, along with the increase of the length of the corrosion area, the elastic deformation buckling critical stress reduction rate of the web corrosion test piece is the largest, and secondly, the edge of a wing is corroded, and the minimum is the turn-up corrosion, which indicates that the influence of the web corrosion on the elastic deformation buckling is the largest.
2. Method for calculating critical stress of elastic deformation buckling
The deformation buckling of the cold-formed thin-walled steel component refers to that a flange-hemming system rotates inwards or outwards around the intersection line of the flange and a web under the action of load, and the web has certain torsion constraint on the flange-hemming system, so that the web generates local buckling, the component generates single-wave or multi-wave deformation buckling deformation along the longitudinal direction, and as shown in fig. 5, the invention considers that the local corrosion cold-formed thin-walled steel column accords with the basic characteristic of the deformation buckling.
The invention discloses a method for calculating the elastic distortion buckling stress of a local corrosion cold-formed thin-walled steel column, which comprises the following specific steps:
S1, obtaining the section parameters of the local corrosion cold-formed thin-walled steel column by equivalent of the uneven thickness of the local corrosion cold-formed thin-walled steel column to uniform thickness;
In order to simplify the calculation formula, the uneven thickness of the plate of the local corrosion steel member is equivalent to the uniform thickness, namely, the influence of the local corrosion is considered through thickness reduction, and the equivalent formula can be expressed by the following formula:
（1）
（2）
（3）
in the method, in the process of the invention, 、AndFor web, flange and bead equivalent thicknesses,、AndFor the thickness of the rust areas of the web, the flange and the curled edge,、AndThe areas of the rust areas of the web plate, the flange and the curled edge are h, b and a, the widths of the web plate, the flange and the curled edge are,The deformation buckling half wavelength of the rustless cold-formed thin-walled steel column is obtained, and t is the original thickness.
The parameters of the section of the local corrosion cold-formed thin-wall steel column are calculated according to the equivalent uniform thickness as follows:
（4）
（5）
（6）
（7）
（8）
（9）
（10）
（11）
in the method, in the process of the invention, The cross section area of the flange-hemming system is rust; is the cross-sectional area of an rustless flange-hemming system; Is a flange-hemming system transverse centroid coordinate; Is the longitudinal centroid coordinate of a flange-hemming system; Is a torsion constant; And Moment of inertia for the cross section to the x-axis and the y-axis; Is the area of the cross-section.
S2, analyzing the stress of the elastic deformation curve Qu Linjie according to a calculation model of the elastic deformation and buckling critical load of the local corrosion cold-formed thin-wall steel column;
According to the distortion buckling critical load calculation model, see fig. 6, a force balance differential equation and a bending moment balance differential equation around the shear center on the x axis and the y axis are respectively established:
（12）
（13）
（14）
in the method, in the process of the invention, Is the elastic modulus; is the shear modulus; polar moment of inertia for the cross section to the origin of the coordinate; And Is displacement of the shear center along the x-axis and y-axis directions; And Transverse and longitudinal to the cross-sectional shear and cross-sectional centroid; The flange-hemming system is a corner of a shearing mandrel; And Respectively a bending constant and a torsion constant of the section; is a critical load for distortion and buckling; is an elastic support reaction force along the y direction; Is a horizontal spring rate; For rotating the spring rate.
Displacement function of distorted buckling in longitudinal direction:
（15）
（16）
in the method, in the process of the invention, AndIs constant.
The flange-hemming system rotates about the resilient support so that displacement of the shear center in the y-axis direction may be accommodated by the cornerThe method comprises the following steps:
（17）
in the method, in the process of the invention, Is z-direction displacement.
Substituting equation (15), equation (16) and equation (17) into equation (12), equation (13) and equation (14) while canceling according to equation (13) and equation (14)Obtaining an equation set:
（18）
（19）
Due to The only condition that the system of equations is zero is that the coefficients of the system of equations are zero, i.e.:
（20）
（21）
s3, obtaining a solution equation of the elastic distortion buckling critical load according to the unique condition that the homogeneous equation set has a non-zero solution, wherein the series determinant is zero;
The only condition that the homogeneous equation set has a non-zero solution is that the series determinant is zero, and the solution equation for obtaining the elastic distortion buckling critical load is obtained by solving:
（22）
S4, stiffness of horizontal spring Stiffness of rotary springHalf wavelength corresponding to buckling critical loadCorrecting to obtain the elastic distortion buckling critical load of the rusted cold-formed thin-walled steel column;
the following corrections are made to the half wavelengths corresponding to the horizontal spring rate, the rotational spring rate and the buckling critical load:
Studies have shown that the web provides a lower horizontal stiffness to the flange-hemming system with little impact on the buckling critical load, and therefore, when calculating the distorted buckling critical load, a horizontal spring rate is assumed 。
The influence of web compressive stress, shearing deformation of a flange-hemming system and corrosion on the stiffness of the rotary spring is considered, and the stiffness of the rotary spring is corrected:
（23）
wherein: For the equivalent stiffness of the web plate, The equivalent compressive stress of the web plate,Is thatAnd (3) the deformation buckling critical load.
Consider the rust to correct the half wavelength:
（24）
equation (23), equation (24) and Substituting the formula (22) to obtain the distortion buckling critical load of the local corrosion cold-formed thin-walled steel member:
（25）
in the method, in the process of the invention, The deformation buckling critical load of the cold-formed thin-walled steel member is locally rusted;、 and The calculation formula for calculating the parameters for the critical load of the distortion buckling is as follows:
（26）
（27）
（28）
in the method, in the process of the invention, AndIn order to calculate the parameters of the device, ， 。
And S5, calculating the elastic distortion buckling critical stress of the local corrosion cold-formed thin-wall section steel according to the elastic distortion buckling critical load.
Calculating the elastic distortion buckling critical stress of the local corrosion cold-formed thin-wall steel according to the elastic distortion buckling critical load, wherein the specific operation is as follows:
（29）
in the method, in the process of the invention, Is the elastic distortion buckling critical stress of the cold-formed thin-walled steel with local corrosion.
3. Comparing the elastic distortion buckling critical stress calculation result with the finite element result
Tables 1-3 show the distortion buckling critical stress calculated in part) And finite element simulation result). In order to study the influence of the corrosion degree on the reliability of the calculation formula of the distortion buckling critical stress, the calculation results of the distortion buckling critical stress of the web plate, the flange and the hemming corrosion thin-walled steel component are respectively compared with the finite element results in fig. 7.
As can be seen by comparing fig. 7 with tables 1-3:
(1) Comparing tables 1-3, it can be seen that, whether the web is rusted or the flange and the hemming are rusted, the calculated buckling critical stress and the finite element simulation result are consistent, particularly the flange and the hemming are rusted, The mean value and the variance are respectively close to 1 and 0, which shows that the calculation of the distortion buckling critical stress of the local corrosion cold-formed thin-wall steel member is reliable.
(2) As can be seen from fig. 7, whether the web is rusted or the flanges and the bead are rusted, as the thickness of the rusted area changes,The fluctuation is about 1, which shows that the calculation rule of the distortion buckling critical stress of the local corrosion cold-formed thin-wall steel member provided by the invention can better reflect the influence rule of the corrosion degree on the distortion buckling critical stress.
Table 1 comparison of the calculation results of the buckling critical stress of the steel member with the rusted web
Note that: H. f and L denote web, flange and hem widths, respectively, e.g., H100F70L10 denotes a steel member having web, flange and hem widths of 100mm, 70mm and 10mm, respectively.
Table 2 comparison of the results of calculation of the critical stress for buckling deformation of the flange-rusted steel member
Table 3 comparison of calculation results of distortion buckling critical stress of hemmed rusted steel member
Therefore, the method for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column is adopted, the formula calculation result is close to the numerical simulation result, and the method can be used for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (6)
1. A calculation method for the elastic distortion buckling critical stress of a local corrosion cold-formed thin-walled steel column is characterized by comprising the following steps:
S1, obtaining the section parameters of the local corrosion cold-formed thin-walled steel column by equivalent of the uneven thickness of the local corrosion cold-formed thin-walled steel column to uniform thickness;
S2, analyzing the stress of the elastic deformation curve Qu Linjie according to a calculation model of the elastic deformation and buckling critical load of the local corrosion cold-formed thin-wall steel column;
s3, obtaining a solution equation of the elastic distortion buckling critical load according to the unique condition that the homogeneous equation set has a non-zero solution, wherein the series determinant is zero;
S4, stiffness of horizontal spring Stiffness of rotary springHalf wavelength corresponding to buckling critical loadCorrecting to obtain the elastic distortion buckling critical load of the rusted cold-formed thin-walled steel column;
And S5, calculating the elastic distortion buckling critical stress of the local corrosion cold-formed thin-wall section steel according to the elastic distortion buckling critical load.
2. The method for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column according to claim 1, wherein in the step S1, the specific operation is as follows:
the partial rust non-uniform thickness is equivalent to the formula of uniform thickness:
（1）
（2）
（3）
in the method, in the process of the invention, 、AndFor web, flange and bead equivalent thicknesses,、AndFor the thickness of the rust areas of the web, the flange and the curled edge,、AndThe areas of the rust areas of the web plate, the flange and the curled edge are h, b and a, the widths of the web plate, the flange and the curled edge are,The deformation buckling half wavelength of the rustless cold-formed thin-walled steel column is obtained, and t is the original thickness;
The parameters of the section of the local corrosion cold-formed thin-wall steel column are calculated according to the equivalent uniform thickness as follows:
（4）
（5）
（6）
（7）
（8）
（9）
（10）
（11）
in the method, in the process of the invention, The cross section area of the flange-hemming system is rust; is the cross-sectional area of an rustless flange-hemming system; Is a flange-hemming system transverse centroid coordinate; Is the longitudinal centroid coordinate of a flange-hemming system; Is a torsion constant; And Moment of inertia for the cross section to the x-axis and the y-axis; Is the area of the cross-section.
3. The method for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column according to claim 1, wherein in the step S2, the specific operation is as follows:
According to the distortion buckling critical load calculation model, respectively establishing a force balance differential equation and a bending moment balance differential equation around the shear center on an x axis and a y axis:
（12）
（13）
（14）
in the method, in the process of the invention, Is the elastic modulus; is the shear modulus; polar moment of inertia for the cross section to the origin of the coordinate; And Is displacement of the shear center along the x-axis and y-axis directions; And Transverse and longitudinal to the cross-sectional shear and cross-sectional centroid; The flange-hemming system is a corner of a shearing mandrel; And Respectively a bending constant and a torsion constant of the section; is a critical load for distortion and buckling; is an elastic support reaction force along the y direction; Is a horizontal spring rate; For the rotational spring rate;
displacement function of distorted buckling in longitudinal direction:
（15）
（16）
in the method, in the process of the invention, AndIs a constant;
The flange-hemming system rotates about the resilient support so that displacement of the shear center in the y-axis direction may be accommodated by the corner The method comprises the following steps:
（17）
in the method, in the process of the invention, Is z-direction displacement;
Substituting equation (15), equation (16) and equation (17) into equation (12), equation (13) and equation (14) while canceling according to equation (13) and equation (14) Obtaining an equation set:
（18）
（19）
Due to The only condition that the system of equations is zero is that the coefficients of the system of equations are zero, i.e.:
（20）
（21）。
4. The method for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column according to claim 1, wherein in the step S3, the only condition that the homogeneous equation set has a non-zero solution is that a series determinant is zero, so as to obtain a solving equation of the elastic distortion buckling critical load:
（22）。
5. The method for calculating the elastic distortion buckling critical stress of the local corrosion cold-formed thin-walled steel column according to claim 1, wherein in the step S4, the horizontal spring stiffness is calculated Stiffness of rotary springHalf wavelength corresponding to buckling critical loadAnd (3) correcting:
the web provides a flange-hemming system with a low horizontal stiffness and a low impact on the buckling critical load, and when calculating the distorted buckling critical load, the horizontal spring stiffness is assumed ；
The influence of web compressive stress, shearing deformation of a flange-hemming system and corrosion on the stiffness of the rotary spring is considered, and the stiffness of the rotary spring is corrected:
（23）
wherein: For the equivalent stiffness of the web plate, The equivalent compressive stress of the web plate,Is thatThe critical load of distortion buckling during the process;
consider the rust to correct the half wavelength:
（24）
wherein: Is the equivalent moment of inertia of the web;
equation (23), equation (24) and Substituting the formula (22) to obtain the distortion buckling critical load of the local corrosion cold-formed thin-walled steel member:
（25）
in the method, in the process of the invention, The deformation buckling critical load of the cold-formed thin-walled steel member is locally rusted;、 and The calculation formula for calculating the parameters for the critical load of the distortion buckling is as follows:
（26）
（27）
（28）
in the method, in the process of the invention, AndIn order to calculate the parameters of the device, ， 。
6. The method for calculating the elastic distortion buckling critical stress of the local corrosion thin-walled steel column according to claim 1, wherein in the step S5, the elastic distortion buckling critical stress of the local corrosion thin-walled steel column is calculated according to the elastic distortion buckling critical load, and the specific operation is as follows:
（29）
in the method, in the process of the invention, Is the elastic distortion buckling critical stress of the cold-formed thin-walled steel with local corrosion.
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