CN110083889B - Diagnostic method for stable bearing capacity of round steel pipe considering constraint of welded hollow ball node - Google Patents
Diagnostic method for stable bearing capacity of round steel pipe considering constraint of welded hollow ball node Download PDFInfo
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Abstract
The invention discloses a method for considering weldingA method for diagnosing the stable bearing capacity of hollow spherical node constrained round steel pipe includes such steps as building multiple calculation models of round steel pipe components by general finite element program ABAQUS. (2) And calculating the stable bearing capacity of the round steel pipe member by adopting a 1-100-order buckling mode as an initial geometric defect. (3) Estimating the mean mu and variance sigma of the total sample data by using the total stable bearing capacity value of each round steel tube component in each buckling mode as the sample data and adopting a maximum likelihood value method 2 . (4) And calculating the design stable bearing capacity of each round steel pipe component based on a unified and reliable method. (5) And obtaining a calculation formula of the design stable bearing capacity of the round steel pipe component by adopting a least square method. The invention can ensure the safety of the space grid structure.
Description
Technical Field
The invention relates to a space grid structure, in particular to a diagnosis method for stabilizing bearing capacity of round steel pipes in the space grid structure under the constraint action of welded hollow sphere nodes.
Background
The space grid structure has the characteristics of large span, light weight, high strength, beautiful shape and the like, and the large-scale public building roof structures such as airport terminal buildings, gymnasiums, auditoriums and the like often adopt the space grid structure. The bearing capacity of the space grid structure is closely related to the mechanical properties of the structural members and the nodes. A large number of rods in the space grid structure bear axle pressure load, and the stable bearing capacity is often a control design factor of the structural rods. The stable bearing capacity of long and thin components has been studied for many years, and there is also a clear regulation in the design specifications of grid structures in various countries. In the current specifications, a column curve is generally adopted to determine the stability coefficient of various sections, and the stability of the pressed component is checked based on the stability coefficient. The pillar curve is calculated with the two free end members taking initial defects into account, and in the actual structure, the influence of the restraint action of the two end nodes of the members on the stability of the axial pressure member is considered by calculating the length coefficient. The value of the length coefficient calculated for the long and thin components in the current specification is mainly based on the node form of the two ends of the components. For example, the technical regulations of the Chinese space grid structure provide that the calculated length coefficient of the chord members of the space grid structure adopting the welded hollow ball nodes is taken as 0.9, the calculated length coefficient of the support web members is taken as 0.9, and the calculated length coefficients of other web members are taken as 0.8; the calculated length coefficients of the chord members and the web members of the space grid structure adopting the bolt ball nodes are all 1.0. The calculated length coefficient value of the axial compression member is related to the constraint function of the node. In fact, the restraining effect of the same node with different dimension specifications on the member is different in the grid structure engineering, and the restraining effect of the node on the member is related to the form, dimension specification and dimension specification of the node and the member. Therefore, the calculated length coefficients of the rod members of the space grid structure adopting various node and rod member specifications should be different. If the actual calculated length coefficient of the rod in the space grid structure is larger than the value specified by the current specification, the stable bearing capacity of the components of the space grid structure designed by the current specification can be overestimated.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for diagnosing the stable bearing capacity of the round steel tube taking the constraint of the welded hollow ball node into consideration, wherein the constraint effect of the node on the structural member can be finely considered, and the safety of the space grid structure is ensured.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the diagnosis method for the stable bearing capacity of the round steel tube in the space grid structure by considering the constraint of the welded hollow ball node comprises the following steps:
(1) A shell unit in a general finite element program ABAQUS is adopted to establish a plurality of round steel pipe component calculation models, the structure of each round steel pipe component model comprises a round steel pipe, the upper end and the lower end of the round steel pipe are respectively welded with a hollow hemispherical node, and the upper end and the lower end of the round steel pipe are respectively welded and fixed with an upper steel plate and a lower steel plate;
(2) The stable bearing capacity of the round steel pipe component is calculated by adopting a buckling mode of 1-100 steps as an initial geometric defect, and the determination process is as follows: applying axial compression load to an upper steel plate in each round steel tube member model, respectively calculating load-displacement curves in the vertical direction at the center point of an upper hemisphere of each round steel tube member by adopting an arc length method and considering the influence of geometric nonlinearity and material nonlinearity, outputting the load-displacement curves in a 1-100-order buckling mode, and selecting the maximum peak point of each axial compression load-displacement curve as a stable bearing capacity value of the round steel tube member;
(3) Attaching each round steel tube member to eachAll stable bearing capacity values under each buckling mode are used as sample data, and a maximum likelihood method is adopted to estimate the average mu and the variance sigma of the total sample data 2 The expression is as follows:
wherein: n is the total number of sample data; x is x i Is the ith data in the sample;
is the average value of the samples;
(4) The design stable bearing capacity of each round steel pipe component is calculated based on a unified and reliable method, and the formula is as follows:
(5) The design stability bearing capacity of each round steel pipe component model is calculated by repeating the steps (1) - (4), the relationship curve graph of the length l of each round steel pipe component, the section wall thickness delta of the round steel pipe component, the section outer diameter D of the round steel pipe component, the hollow hemispherical node wall thickness t, the hollow spherical node outer diameter D and the relationship curve graph of the round steel pipe, the hollow spherical node materials and the round steel pipe component design stability bearing capacity are respectively drawn by using Origin software, the influence of the parameters on the round steel pipe design stability bearing capacity is respectively analyzed by using Origin software, then the relationship between the round steel pipe design stability bearing capacity and the parameters is quantitatively determined by adopting a linear regression method, and finally the following round steel pipe component design stability bearing capacity calculation formula is obtained by adopting a least square method:
wherein f is the design strength value of the round steel pipe component and the hollow ball joint material.
The beneficial effects of the invention are as follows:
the restraining effect of the same node with different dimension specifications on the component in the grid structure engineering is different, and the restraining effect of the node on the component is related to the form, dimension specification and dimension specification of the rod piece. Therefore, the calculated length coefficients of the rod members of the space grid structure adopting various node and rod member specifications should be different. If the actual calculated length coefficient of the rod in the space grid structure is larger than the value specified by the current specification, the stable bearing capacity of the components of the space grid structure designed by the current specification can be overestimated. In order to ensure the safety of the structure, the invention finely considers the constraint effect of the nodes on the structural rod piece, and establishes a finely calculating method of the component bearing capacity taking the actual constraint effect of the nodes into consideration.
Drawings
FIG. 1 is a mechanical diagnostic model of a welded hollow sphere joint in the present invention;
FIG. 2 is a graph of the overall process of displacement, which is calculated by taking the model No. 4 in Table 2, which takes the 1 st order buckling mode as an initial defect mode, and considers the nonlinearity and the geometric nonlinearity of materials, of the load axial pressure load of the round steel pipe member;
FIG. 3 is a graph of the design stability load bearing capacity of a round steel tube member versus the length l of the round steel tube;
FIG. 4 is a plot of the design stability load bearing capacity of a round steel tube member versus the wall thickness delta of the round steel tube;
FIG. 5 is a graph showing the relationship between the design stable bearing capacity of a round steel pipe member and the outer diameter d of the section of the steel pipe;
FIG. 6 is a plot of the design stable bearing capacity of a round steel tube member versus the hollow sphere node wall thickness t;
FIG. 7 is a graph of the design stable bearing capacity of a round steel tube member versus the outer diameter D of a hollow sphere node;
FIG. 8 is a graph showing the relationship between the design stability bearing capacity of a round steel tube member and the design strength value f of the round steel tube member and hollow ball joint material;
FIG. 9 is a dimensionless variable D 2 Delta l and dimensionless variable P crd /πfd 2 A relationship curve;
Detailed Description
The present invention will be described in detail with reference to specific examples.
The diagnosis method for the stable bearing capacity of the round steel tube considering the constraint of the welded hollow ball node in the space grid structure comprises the following steps:
(1) A plurality of round steel pipe component calculation models are established by adopting a shell unit in a general finite element program ABAQUS, the structure of each round steel pipe component model comprises a round steel pipe, the upper end and the lower end of the round steel pipe are respectively welded with a hollow hemispherical node, the upper end and the lower end of the round steel pipe are respectively welded and fixed with an upper steel plate and a lower steel plate, and the finite element numerical model is shown in figure 1.
Because the upper hemisphere and the lower hemisphere which form the welded hollow sphere node in the actual model are rigidly connected, only the hemispherical model and the rigid connection supporting seat condition can be established in the calculation model. The hemispherical nodes at two ends of the round steel pipe are welded and fixed with the upper steel plate and the lower steel plate respectively, so that the spherical nodes can be used for simulating the stress condition of the spatial structure round steel pipe rod piece taking the constraint action of the welded hollow spherical nodes into consideration.
(2) The stable bearing capacity of the round steel pipe component is calculated by adopting a buckling mode of 1-100 steps as an initial geometric defect, and the determination process is as follows: and applying axial compressive load to the upper steel plate in each round steel pipe member model, respectively calculating load-displacement curves at the center point of the upper hemisphere of each round steel pipe member by adopting an arc length method and considering the influence of geometric nonlinearity and material nonlinearity, wherein the displacement is along the vertical displacement of the steel pipe, outputting load-displacement curves under a 1-100-order buckling mode, and selecting the maximum peak point of each axial compressive load-displacement curve as a stable bearing capacity value of the round steel pipe member. Fig. 2 shows a graph of axial load versus displacement.
(3) Estimating the mean mu and variance sigma of the total sample data by using the total stable bearing capacity value of each round steel tube component in each buckling mode as the sample data and adopting a maximum likelihood value method 2 The expression is as follows:
wherein: n is the total number of sample data; x is x i Is the ith data in the sample;
mean value of samples
The derivation of this formula is described in (initial defective single layer net shell ultimate bearing capacity analysis, ding Yang, taking into account rod instability) 1,2 Ji Lin, ji Lin 1 Yang Lvlei, yang Lvlei 1 Li Zhongxian, li Zhongxian 1,2 University of Tianjin journal, vol.44 No.12 dec.2011).
The derivation of this formula is briefly described below:
in the first step, the ultimate bearing capacity of the grid structure member welded with the hollow ball nodes is considered to be subjected to normal distribution. Further verification was performed using a nonparametric hypothesis test, and the present invention uses the K-S (Kolmogorov-Smimev) test method. Let the sample cumulative frequency distribution function be g n (x)，g n (x) Obeying the theoretical distribution function g (x), the K-S test statistic is
With 0.050 as a test level, carrying out hypothesis test on stable bearing capacity distribution of the round steel tube component model n =0.050, if p>And 0.050, the stable bearing capacity of the round steel pipe component under the constraint action of the node is subjected to normal distribution.
Secondly, verifying that the stable bearing capacity of the round steel pipe component considering the node constraint effect in the previous step obeys normal distribution, so that the probability density function of the stable bearing capacity of the round steel pipe component is as follows:
where x is a random variable, here the stable bearing capacity of a round steel pipe.
Constructing a likelihood function:
establishing an equation set:
solving equation set (5) to obtain:
(4) The design stable bearing capacity of each round steel pipe component is calculated based on a unified and reliable method, and the formula is as follows:
namely: defining the design stability bearing capacity P of the round steel pipe component with the initial geometric defect considering the node constraint crd The standard deviation estimate is subtracted by a factor of 2 from the overall mean estimate.
Calculating P of the above formula (6) crd The reliability of (2) is 0.977.P (P) crd See (analysis of initial defective single layer net shell ultimate bearing capacity considering rod instability, ding Yang) 1,2 Ji Lin, ji Lin 1 Yang Lvlei, yang Lvlei 1 Li Zhongxian 1,2 University of Tianjin journal, vol.44 No.12 dec.2011).
(5) And (3) repeating the steps (1) - (4) to calculate the design stability bearing capacity of each round steel pipe member model, respectively drawing a relation curve chart of the length l of each round steel pipe member, the section wall thickness delta of the round steel pipe member, the section outer diameter D of the round steel pipe member, the hollow hemispherical node wall thickness t, the hollow spherical node outer diameter D and the design stability bearing capacity of the round steel pipe, the hollow spherical node materials and the round steel pipe member by using Origin software, and respectively analyzing the influence of the parameters on the design stability bearing capacity of the round steel pipe by using Origin software. And then quantitatively determining the relation between the design stable bearing capacity of the round steel pipe and the parameters by adopting a linear regression method, and finally obtaining a calculation formula (7) of the design stable bearing capacity of the round steel pipe component by adopting a least square method. And in the analysis of the figure 9, the linear correlation coefficient of the two dimensionless variables is close to 1 and is 0.972, so that the two dimensionless variables are known to form a linear relationship, and the design stability bearing capacity calculation formula (7) of the round steel pipe member is proved to be reasonable.
Wherein f is the design strength value of the round steel pipe component and the hollow ball joint material.
Therefore, a refined component bearing capacity calculation method considering the actual constraint action of the nodes is established, and the stress condition of the round steel pipe rod piece in the space grid structure under the constraint action of the nodes is diagnosed through the mechanical diagnosis model in the steps so as to ensure the safety of the space grid structure.
Example 1
(1) A plurality of round steel pipe component calculation models are established by adopting a shell unit in a general finite element program ABAQUS, the structure of each round steel pipe component model comprises a round steel pipe, the upper end and the lower end of the round steel pipe are respectively welded with a hollow hemispherical node, the upper end and the lower end of the round steel pipe are respectively welded and fixed with an upper steel plate and a lower steel plate, and the finite element numerical model is shown in figure 1.
Considering the constraint effect of welding hollow ball nodes at two ends, factors which may influence the stable bearing capacity of the space structure round steel pipe rod piece include: the length l, the section wall thickness delta and the section outer diameter d of the round steel pipe rod piece; the wall thickness t and the outer diameter D of the hollow sphere node; round steel pipe components and materials for welding hollow ball joints. To quantitatively analyze the influence of each parameter on the stable bearing capacity of the round steel pipe member, a finite element numerical model was built based on each parameter listed in table 2 for parameterization analysis.
Table 1 parameters of round steel tube rod pieces considering node constraint
(2) An axial compression load is applied to 54 numerical models in table 2, each model introduces a buckling mode of 1-100 orders of the model as an initial geometric defect, and an arc length method is adopted to respectively calculate a load-displacement curve of each defective round steel pipe component by considering the influence of geometric nonlinearity and material nonlinearity. For example, fig. 2 is a full-process curve of displacement, which is calculated by taking the 1 st-order buckling mode as an initial defect mode and considering the nonlinearity and the geometric nonlinearity of the material, of the round steel pipe member load axial pressure load in the model No. 4 in table 2. And taking the maximum peak point of the axial pressure load-displacement curve as the stable bearing capacity value of the round steel pipe component.
(3) And calculating the stable bearing capacity of the round steel pipe member by adopting a buckling mode of 1-100 steps as an initial geometric defect, wherein each round steel pipe member with the specification in table 1 corresponds to 100 stable bearing capacity values. Take model number 4 in table 1 as an example. The 100 th order buckling mode was calculated as the initial geometric defect form of the round steel tube member. And calculating the stability limit bearing capacity of the initial geometric defect round steel pipe component finite element model considering the constraint of the welded hollow ball node, and obtaining a stability bearing capacity sample of the No. 4 round steel pipe component, wherein the sample capacity is 100. From the sample distribution, the overall distribution of the stable bearing capacity of the round steel tube member taking into account the node constraint can be estimated.
(4) Using maximum likelihood value method to take peak point of each axle load-displacement curve selected in step (2) as stable bearing capacity value of the initial geometric defect round steel tube component, taking these obtained stable bearing capacity values as mean mu and variance sigma of sample data estimation population 2 The expression is as follows:
wherein: n is the total number of sample data; x is x i Is the ith data in the sample;
is the average value of the samples.
It is assumed that the ultimate bearing capacity of the mesh structural member of the welded hollow sphere node is considered to be subject to normal distribution. Further validation was performed using a nonparametric hypothesis test, herein using the K-S (Kolmogorov-Smimev) test method.
Let the sample cumulative frequency distribution function be g n (x)，g n (x) Obeying the theoretical distribution function g (x), the K-S test statistic is
The K-S test steps are as follows: (1) establishing zero hypothesis H 0 Sample cumulative frequency distribution function g n (x) Calculating T based on sample data following a theoretical distribution function g (x) (2) n A value; (3) adopting a significance level alpha as a test level; (4) calculating and sampling based on theoretical distribution function g (x) to obtain large T n Value, and greater value of T n Probability p of (2); (5) make a judgment if p<Alpha, according to the small probability anti-evidence method, the assumption of zero is refused to accept H based on the effect that the theoretical distribution function g (x) should not appear in the test sample in one sample 0 The method comprises the steps of carrying out a first treatment on the surface of the Conversely, accept zero hypothesis H 0 。
With 0.050 as a test level, carrying out hypothesis test on stable bearing capacity distribution of the No. 4 round steel tube component model n ＝0.050，p＝0.675，p>0.050, so that the stable bearing capacity of the round steel pipe component taking the node constraint action into consideration obeys normal distribution.
Estimating the mean mu and variance sigma of the population from the sample data using maximum likelihood method 2 The probability density function of the stable bearing capacity of the round steel pipe component is as follows:
where x is a random variable, here the stable load bearing capacity of the round steel tubular member.
Constructing a likelihood function:
establishing an equation set:
solving equation set (5) to obtain:
(5) The design stable bearing capacity of each round steel pipe component is calculated based on a unified and reliable method, and the formula is as follows:
calculating the above P crd The reliability of (2) is 0.977.
(6) The stability limit bearing capacity of the 54 groups of round steel tube members can be calculated by repeating the steps (1) to (5) as shown in table 2.
Table 2 stability limit bearing capacity of round steel tube member
(7) And respectively analyzing the influences of the length l of the round steel pipe, the wall thickness delta of the section of the round steel pipe, the outer diameter D of the section of the round steel pipe, the wall thickness t of the joint of the welded hollow ball, the outer diameter D of the joint of the welded hollow ball and the material of the joint of the round steel pipe and the welded hollow ball on the design stable bearing capacity of the round steel pipe member, and quantitatively determining the relation between the design stable bearing capacity of the round steel pipe member and each parameter by adopting a linear regression method to obtain a practical calculation formula of the design stable bearing capacity of the round steel pipe member.
The design stability load capacities of the round steel tube member models of the respective specifications listed in table 2 are listed in table 3. Only the length l of the round steel pipe in each parameter of the model 1 to 10 is changed, and the other parameters are the same. The design stable bearing capacity of the model 1-10 is taken as an ordinate, the length l of the round steel pipe is taken as an abscissa, and a relation curve of the design stable bearing capacity of the round steel pipe component and the length l of the round steel pipe can be obtained, as shown in figure 3. As can be seen from fig. 3, the design stability bearing capacity of the round steel pipe member decreases with the increase in the length of the round steel pipe. Only the wall thickness of the section of the round steel tube in each parameter of the model No. 11-20 is changed, and the other parameters are the same. The design stable bearing capacity of the model of 11-20 is taken as an ordinate, the wall thickness delta of the cross section of the round steel tube is taken as an abscissa, and the design stable bearing capacity of the round steel tube component and the round steel tube cross section component can be increased. Only the external diameter d of the cross section of the round steel tube is changed in each parameter of the model No. 21-30, and the other parameters are the same. The design stable bearing capacity of the model No. 21-30 is taken as an ordinate, the external diameter d of the cross section of the round steel tube is taken as an abscissa, and a relation curve of the design stable bearing capacity of the round steel tube component and the external diameter d of the cross section of the steel tube can be obtained, as shown in figure 5. As can be seen from fig. 5, the design stability bearing capacity of the round steel pipe member increases with the increase of the outer diameter of the cross section of the round steel pipe. Only the wall thickness t of the welded hollow sphere node in each parameter of the model numbers 31 to 40 is changed, and the other parameters are the same. And the design stable bearing capacity of the model No. 31-40 is taken as an ordinate, the wall thickness t of the welded hollow ball joint is taken as an abscissa, and a relation curve of the design stable bearing capacity of the round steel pipe component and the wall thickness t of the welded hollow ball joint can be obtained, as shown in figure 6. As can be seen from fig. 6, the design stability bearing capacity of the round steel pipe member remains unchanged with the increase of the wall thickness of the welded hollow sphere joint. Only the outer diameter D of the welded hollow ball node in each parameter of the model No. 41-50 is changed, and the other parameters are the same. And the design stable bearing capacity of the model No. 41-50 is taken as an ordinate, the outer diameter D of the welded hollow ball node is taken as an abscissa, and a relation curve of the design stable bearing capacity of the round steel pipe component and the outer diameter D of the welded hollow ball node can be obtained, as shown in figure 7. As can be seen from fig. 7, the design stability bearing capacity of the round steel pipe member increases and decreases with the increase of the outer diameter of the welded hollow ball joint. Only the design strength values of the round steel pipe and the welded hollow ball node material are changed in all parameters of the model No. 51-54, and the other parameters are the same. And the design stable bearing capacity of the model No. 51-54 is taken as an ordinate, the design strength value f of the round steel pipe and the welding hollow ball joint material is taken as an abscissa, and a relation curve of the design stable bearing capacity of the round steel pipe component and the design strength value f of the round steel pipe and the welding hollow ball joint material can be obtained, as shown in figure 8. As can be seen from fig. 8, the design stability bearing capacity of the round steel pipe member increases with the increase of the design strength value f of the round steel pipe and welded hollow ball joint material.
(8) In the form of dimensionless variables D 2 Delta l is the abscissa, and the dimensionless variable P crd /πfd 2 The graph is plotted on the ordinate as shown in fig. 9. Analysis of FIG. 9 shows that the two dimensionless variables are in linear relationship, the linear correlation coefficient is 0.972, and the least square method is adopted to obtain P crd The linear regression formula of (2) is
The stable bearing capacities of the round steel pipe members No. 2, no. 13, no. 26, no. 36, no. 43 and No. 53 in Table 1 are calculated respectively by the method and the comparison file (comparison file 1: "GB 55017-2014 steel structure design Specification") (see Table 4)
Table 4 specification and round steel tube member stability bearing capacity calculated by the methods herein
As can be seen from Table 4, the stable bearing capacities of the No. 2, no. 36, no. 43 and No. 53 round steel tube members calculated by the standard method are smaller than the calculated result by the method, wherein the relative difference of the stable bearing capacities of the No. 43 round steel tube members calculated by the two methods reaches-29.35%. The stable bearing capacity of the No. 13 round steel pipe component and the No. 26 round steel pipe component calculated by the standard method is larger than the calculated result by the method, wherein the relative difference of the stable bearing capacities of the No. 13 round steel pipe component calculated by the two methods reaches 18.93 percent. Therefore, the stable bearing capacity of the space structure round steel pipe component is greatly different from a standard calculated value when the constraint action of the welding hollow ball nodes at the two ends is finely considered.
The current design method is unreasonable: the main expression is as follows: the stability bearing capacity of the round steel pipe rod piece calculated by directly adopting the unified calculation length coefficient can be larger or smaller than that of the actual situation by neglecting the constraint effect difference of the welded hollow ball nodes with different specifications. If the standard calculation value is smaller, a round steel pipe component with larger specification is required to be adopted in the design, so that the design is uneconomical; if the standard calculation value is larger, a smaller-specification round steel pipe member may be adopted in the design, so that the design is unsafe.
By comparison with the specification: the scientific and reasonable structural design method should finely consider the different restraining actions of the welded hollow ball nodes with different specifications on the round steel pipe rod piece, and accurately consider the restraining action of the end nodes when determining the stable bearing capacity of the round steel pipe component.
Claims (1)
1. The diagnosis method considering the stable bearing capacity of the round steel pipe constrained by the welded hollow ball node comprises the following steps:
(1) A shell unit in a general finite element program ABAQUS is adopted to establish a plurality of round steel pipe component calculation models, the structure of each round steel pipe component model comprises a round steel pipe, the upper end and the lower end of the round steel pipe are respectively welded with a hollow hemispherical node, and the upper end and the lower end of the round steel pipe are respectively welded and fixed with an upper steel plate and a lower steel plate;
(2) The stable bearing capacity of the round steel pipe component is calculated by adopting a buckling mode of 1-100 steps as an initial geometric defect, and the determination process is as follows: applying axial compression load to an upper steel plate in each round steel tube member model, respectively calculating load-displacement curves in the vertical direction at the center point of an upper hemisphere of each round steel tube member by adopting an arc length method and considering the influence of geometric nonlinearity and material nonlinearity, outputting the load-displacement curves in a 1-100-order buckling mode, and selecting the maximum peak point of each axial compression load-displacement curve as a stable bearing capacity value of the round steel tube member;
(3) The total stable bearing capacity value of each round steel tube component in each buckling mode is used as sample data by adopting a maximum likelihood value methodEstimating the mean mu and variance sigma of the sample data population 2 The expression is as follows:
wherein: n is the total number of sample data; x is x i Is the ith data in the sample;
is the average value of the samples;
(4) The design stable bearing capacity of each round steel pipe component is calculated based on a unified and reliable method, and the formula is as follows:
(5) The design stability bearing capacity of each round steel pipe component model is calculated by repeating the steps (1) - (4), the relationship curve graph of the length l of each round steel pipe component, the section wall thickness delta of the round steel pipe component, the section outer diameter D of the round steel pipe component, the hollow hemispherical node wall thickness t, the hollow spherical node outer diameter D and the relationship curve graph of the round steel pipe, the hollow spherical node materials and the round steel pipe component design stability bearing capacity are respectively drawn by using Origin software, the influence of the parameters on the round steel pipe design stability bearing capacity is respectively analyzed by using Origin software, then the relationship between the round steel pipe design stability bearing capacity and the parameters is quantitatively determined by adopting a linear regression method, and finally the following round steel pipe component design stability bearing capacity calculation formula is obtained by adopting a least square method:
wherein f is the design strength value of the round steel pipe component and the hollow ball joint material.
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