CN113420388A - All-welded integral node tearing path calculation method based on fitting Mises yield criterion - Google Patents

All-welded integral node tearing path calculation method based on fitting Mises yield criterion Download PDF

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CN113420388A
CN113420388A CN202110682741.2A CN202110682741A CN113420388A CN 113420388 A CN113420388 A CN 113420388A CN 202110682741 A CN202110682741 A CN 202110682741A CN 113420388 A CN113420388 A CN 113420388A
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web member
plate
stress
horizontal plate
web
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CN113420388B (en
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谢兰博
康晋
徐伟
刘汉顺
段雪炜
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China Railway Major Bridge Reconnaissance and Design Institute Co Ltd
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China Railway Major Bridge Reconnaissance and Design Institute Co Ltd
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Abstract

The invention relates to a method for calculating a tearing path of an all-welded integral node based on a fitting Mises yield criterion, which comprises the steps of defining theoretical equivalent allowable stress based on the Mises yield criterion so that the theoretical equivalent allowable stress considers normal stress and shear stress on an oblique line; fitting the theoretical equivalent allowable stress to obtain a fitted equivalent allowable stress; defining a web member horizontal plate coefficient based on the fitted equivalent allowable stress; and calculating the tearing path corresponding to the web member based on the horizontal plate coefficient of the web member. The combined action of axial stress and shearing stress on a tearing path is considered, and the accuracy of a calculation result can be effectively improved.

Description

All-welded integral node tearing path calculation method based on fitting Mises yield criterion
Technical Field
The invention relates to the technical field of bridge steel structures, in particular to a calculation method of an all-welded integral node tearing path based on a fitting Mises yield criterion.
Background
The steel truss girder has excellent integral and local rigidity and is widely applied to various bridge types. With the improvement of construction technology, when the main girder is a steel truss girder, the whole section hoisting construction is generally adopted for shortening the construction period, and the main girder is generally an all-welded integral node at the moment.
The stress calculation methods described in the relevant specifications (TB 10091-.
The related art (CN112699448A) refers to a calculation method for tearing of integral node of all-welded steel truss girder, which assumes that the axial allowable stress of steel is the shear allowable stress
Figure BDA0003120078300000011
Taking the two less favorable ones without considering the combined action of the shear stress and the axial stress on the tearing path, and giving equivalent allowable stress on the oblique line tearing path and various common node tearing path calculation formulas based on the assumption. However, the related art (CN112699448A) does not consider the combined action of the shear stress and the axial stress on the tear path, so that the calculation result is biased to be unsafe, and the safety factor may need to be artificially increased during actual calculation, so that the calculation method has certain limitations.
In order to solve the above problems, there is a need to develop a tearing path calculation method for an all-welded integral node, which is convenient to calculate and can simultaneously consider axial and shear stresses on a tearing path.
Disclosure of Invention
The embodiment of the invention provides a method for calculating a tearing path of an all-welded integral node based on a fitting Mises yield criterion, which considers the combined action of axial stress and shearing stress on the tearing path and can effectively improve the safety coefficient of a calculation result.
The embodiment provides a method for calculating a tearing path of an all-welded integral node based on a fitting Mises yield criterion, which comprises the following steps of: defining theoretical equivalent allowable stress based on Mises yield criterion so that the theoretical equivalent allowable stress considers normal stress and shear stress on a diagonal line; fitting the theoretical equivalent allowable stress to obtain a fitted equivalent allowable stress; defining a web member horizontal plate coefficient based on the fitted equivalent allowable stress; and calculating the tearing path corresponding to the web member based on the horizontal plate coefficient of the web member.
In some embodiments, defining a theoretical equivalent allowable stress based on the Mises yield criterion such that the theoretical equivalent allowable stress accounts for both normal and shear stresses on the diagonal, comprises the steps of: acquiring normal stress and shear stress on the oblique line; the calculation formula of the normal stress on the oblique line is as follows:
Figure BDA0003120078300000021
the calculation formula of the shear stress on the oblique line is as follows:
Figure BDA0003120078300000022
wherein, sigma is the positive stress on the oblique line, tau is the shearing stress on the oblique line, delta is the structure thickness, T is the tension, alphaxThe included angle between the tearing path and the perpendicular line of the stress direction is shown, and l is the length of the oblique line;
and converting the normal stress and the shear stress on the oblique line into equivalent allowable stress on the oblique line according to the Mises yield criterion.
In some embodiments, converting the normal stress and the shear stress on the oblique line into an equivalent allowable stress on the oblique line according to the Mises yield criterion comprises the steps of: obtaining a conversion stress calculation formula on the oblique line according to the Mises yield criterion; the calculation formula of the converted stress on the oblique line is as follows:
Figure BDA0003120078300000023
defining a theoretical equivalent allowable stress based on a conversion stress calculation formula on the oblique line;
the calculation formula of the theoretical equivalent allowable stress is as follows:
Figure BDA0003120078300000024
wherein the content of the first and second substances,
[σ]0xfor theoretical equivalent allowable stress, [ sigma ]]The material is substantially stress tolerant.
In some embodiments, fitting the theoretical equivalent allowable stress to obtain a fitted equivalent allowable stress coefficient includes: carrying out linear fitting processing on the calculation formula of the theoretical equivalent allowable stress under the same boundary condition to obtain fitted equivalent allowable stress; the calculation formula of the fitting equivalent allowable stress is as follows:
Figure BDA0003120078300000031
where η is the fitting coefficient.
In some embodiments, the calculation formula of the web member horizontal plate coefficient is:
Figure BDA0003120078300000032
wherein the content of the first and second substances,
δyis the web member horizontal plate thickness, alphayFor web member horizontal plate dovetail plate corner cut, RyFor rounding the web-member horizontal-plate dovetail-plate with an arc radius, delta0Is the gusset plate thickness.
In some embodiments, the web member is an H-section web member, and the two sides of the web member riser are symmetrical bevel edges; calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of: calculating a tearing path corresponding to the web member according to a first formula;
the first formula is:
Figure BDA0003120078300000033
wherein L is1、L2And L3The smaller value in (A) is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the height of the web member vertical plate, H is the projection length of the intersection point of the web member vertical plate symmetrical bevel edge and the web member vertical plate to the end distance in the web member horizontal plate node on the web member axis, and Λ is the coefficient of the web member horizontal plate, alphafIs the included angle between the bevel edge of the web member vertical plate and the axis of the web member.
In some embodiments, the web member is an H-shaped section web member, and the two sides of the web member riser are arc edges; calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of: calculating a tearing path corresponding to the web member according to a second formula;
the second formula is:
Figure BDA0003120078300000041
wherein L is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the height of the web member vertical plate, and R is1And R2Are respectively the arc radii of two sides of the web member vertical plate H1And H2The projection lengths of the distances from arc starting points of arc edges on two sides of the web member vertical plate to the inner end part of the web member horizontal plate gusset plate on the axis of the web member are respectively, and the lambada is the coefficient of the web member horizontal plate.
In some embodiments, the web member is a box section web member with the web riser flanked by symmetrically beveled edges; calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of: calculating a tearing path corresponding to the web member according to a third formula; the third formula is:
Figure BDA0003120078300000042
wherein L is1、L2And L3The smaller value is to convert the horizontal plate of the web member to the gusset plateD is the sum of the distances from the inner sides of the upper horizontal plate and the lower horizontal plate of the web member to the edges of the vertical plates, H is the projection length of the distance from the symmetrical inclined edges of the web member vertical plates and the web member vertical plates to the inner end part of the node of the web member horizontal plate on the axis of the web member, D is the net distance of the upper horizontal plate and the lower horizontal plate of the web member, Λ is the coefficient of the web member horizontal plate, and alpha is the sum of the height of the web member horizontal platefIs the included angle between the bevel edge of the web member vertical plate and the axis of the web member.
In some embodiments, the web member is a box section web member, and the two sides of the web member vertical plate are symmetrical circular arc edges; calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of: calculating a tearing path corresponding to the web member according to a fourth formula; the fourth formula is:
Figure BDA0003120078300000051
l is the shortest tearing path length of converting the web member horizontal plate to the gusset plate, D is the sum of distances from the inner sides of the upper and lower horizontal plates of the web member to the edge of the vertical plate, R is the arc radius of the two sides of the web member vertical plate, H is the projection length of the arc starting point of the arc edge of the web member vertical plate to the distance from the inner end part of the gusset plate of the web member horizontal plate on the axis of the web member, D is the net distance of the upper and lower horizontal plates of the web member, and Lambda is the coefficient of the web member horizontal plate.
In some embodiments, the web member is an H-shaped section web member, and asymmetric arc edges are arranged on two sides of a web member riser; calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of: calculating a tearing path corresponding to the web member according to a fifth formula; the fifth formula is:
Figure BDA0003120078300000052
wherein, L (h)1,h2) The minimum value of (A) is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the sum of the distances from the inner sides of the upper and lower horizontal plates of the web member to the edge of the vertical plate, R1And R2Are respectively the arc radii of two sides of the web member vertical plate H1Is a web member vertical plate halfDiameter of R1The projection length of the distance from the arc starting point of the arc edge to the inner end part of the node plate of the horizontal plate of the web member on the same side on the axis of the web member, H2The vertical plate radius of the web member is R2The projection length of the distance from the arc starting point of the arc edge to the inner end part of the node plate of the horizontal plate of the web member on the same side on the axis of the web member, H0The projection distance of the inner end parts of the upper horizontal plate node plate and the lower horizontal plate node plate of the web member on the axis of the web member, D is the net distance of the upper horizontal plate and the lower horizontal plate of the web member, Lambda is the coefficient of the horizontal plate of the web member, h1And h2Is a variable, LhThe (h, R) function is LβThe (beta) function being [0,0.5 pi ] with respect to beta]Defining a minimum value within the domain; the function LβThe formula for the calculation of (. beta.) is:
Figure BDA0003120078300000053
wherein beta is a value within [0,0.5 pi ].
The embodiment of the invention carries out linear fitting treatment on the equivalent allowable stress of the diagonal path obtained based on the Mises yield criterion to obtain the fitting equivalent allowable stress, obtains the horizontal plate coefficient of the web member according to the fitting equivalent allowable stress, and provides the calculation method for the tearing path of the web member. The combined action of axial stress and shearing stress on the tearing path is considered, the calculation is convenient, and the calculated tearing path length is more reasonable.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic flow chart of a calculation method of an all-welded integral node tear path based on a fitting Mises yield criterion according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of parameters calculated by tearing the structure along an oblique line according to an embodiment of the present invention;
FIG. 3 is a comparison of the fitting process and the theoretical equivalent allowable stress factor provided by an embodiment of the present invention;
FIG. 4 is a comparison of the fitting process and the theoretical equivalent allowable stress coefficient error provided by an embodiment of the present invention;
FIG. 5 is a schematic diagram illustrating parameters for calculating tear paths of horizontal plates of web members according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of web member parameters under a first operating condition according to an embodiment of the present invention;
FIG. 7 is a schematic view of web parameters under a second operating condition according to an embodiment of the present invention;
FIG. 8 is a schematic view of web parameters under a third operating condition according to an embodiment of the present invention;
fig. 9 is a schematic diagram of the parameters of a web member under a fourth condition according to the embodiment of the present invention;
FIG. 10 is a schematic view of a web bar parameter under a fifth operating condition according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
As shown in fig. 1, an embodiment of the present invention provides a method for calculating an all-welded integral node tear path based on a fitting Mises yield criterion, including the steps of:
s100, defining theoretical equivalent allowable stress based on Mises yield criterion to enable the theoretical equivalent allowable stress to consider normal stress and shear stress on an oblique line;
s200, fitting the theoretical equivalent allowable stress under the same boundary condition to obtain a fitted equivalent allowable stress;
s300, defining a horizontal plate coefficient of the web member based on the fitted equivalent allowable stress;
and S400, calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member.
It should be noted that, because the theoretical equivalent allowable stress takes into account the normal stress and the shear stress on the oblique line, based on this, the combined action of the shear stress and the axial stress on the tear path can be taken into account when the tear path is subsequently calculated, thereby improving the accuracy of the calculation result.
In this embodiment, a linear fitting process is performed on the equivalent allowable stress of the diagonal path obtained based on the Mises yield criterion to obtain a fitted equivalent allowable stress, a horizontal plate coefficient of the web member is obtained according to the fitted equivalent allowable stress, and a calculation method for the tearing path of the web member is provided. The combined action of axial stress and shearing stress on the tearing path is considered, the calculation is convenient, and the calculated tearing path length is more reasonable.
In some embodiments, step S100 comprises the steps of:
s110, acquiring the normal stress and the shear stress on the oblique line;
the calculation formula of the normal stress on the oblique line is as follows:
Figure BDA0003120078300000071
the calculation formula of the shear stress on the oblique line is as follows:
Figure BDA0003120078300000081
as shown in FIG. 2, σ is the normal stress on the diagonal, τ is the shear stress on the diagonal, δ is the structural thickness, T is the tension, αxThe included angle between the tearing path and the perpendicular line of the stress direction is shown, and l is the length of the oblique line;
and S120, converting the normal stress and the shear stress on the oblique line into equivalent allowable stress on the oblique line according to the Mises yield criterion.
Preferably, the step S120 includes the steps of:
s121, obtaining a conversion stress calculation formula on the oblique line according to the Mises yield criterion;
the calculation formula of the converted stress on the oblique line is as follows:
Figure BDA0003120078300000082
s122, defining theoretical equivalent allowable stress based on a conversion stress calculation formula on the oblique line;
the calculation formula of the theoretical equivalent allowable stress is as follows:
Figure BDA0003120078300000083
wherein the content of the first and second substances,
[σ]0xfor theoretical equivalent allowable stress, [ sigma ]]The material is substantially stress tolerant.
Thus, the theoretical equivalent allowable stress coefficient is:
Figure BDA0003120078300000084
in some embodiments, step S200 includes the steps of: carrying out linear fitting processing on the calculation formula of the theoretical equivalent allowable stress under the same boundary condition to obtain fitted equivalent allowable stress;
the calculation formula of the fitting equivalent allowable stress is as follows:
[σ]x＝(1-ηsinαx)[σ]，
Figure BDA0003120078300000085
where η is the fitting coefficient.
The boundary conditions are as follows: when alpha isxWhen equal to 0, [ sigma ]]x＝[σ](ii) a When alpha isxWhen the angle is equal to 90 degrees,
Figure BDA0003120078300000086
Figure BDA0003120078300000087
therefore, the fitted equivalent allowable stress coefficient after the fitting process is:
lx＝(1-ηsinαx)，
Figure BDA0003120078300000088
where η is the fitting coefficient.
The present embodiment takes into account the theoretical equivalent allowable stress [ sigma ]]xMiddle sin alphaxThe method is not a linear function, a calculation formula is not easy to obtain for common web member tearing paths, so that the method is difficult to use and has no practical value for complex nodes, and the fitting equivalent allowable stress which is convenient to calculate is obtained by adopting a fitting mode.
The defined error is:
Figure BDA0003120078300000091
as shown in fig. 3 and 4:
the fitting equivalent allowable stress coefficient after fitting treatment is mostly smaller than the theoretical equivalent allowable stress coefficient, namely is more safe, and the error between the fitting equivalent allowable stress coefficient after fitting treatment and the theoretical equivalent allowable stress coefficient is alphaxGreater than 55 deg. and not more than 0.5%, alphaxWhen the temperature is less than 55 degrees, the maximum error is about-5 percent, so that the equivalent allowable stress coefficient after fitting treatment is adopted for calculation, and the safety of the tearing path result can be effectively improved.
In some embodiments, the calculation formula of the horizontal plate coefficient of the web member in S300 is:
Figure BDA0003120078300000092
wherein the content of the first and second substances,
δyis the web member horizontal plate thickness, alphayFor web member horizontal plate dovetail plate corner cut, RyFor rounding the web-member horizontal-plate dovetail-plate with an arc radius, delta0Is the gusset plate thickness.
In the embodiment, when the tear path of the node is actually calculated, the node plate and the horizontal plate of the web member are usually damaged together, and the length of the tear path of the horizontal plate of the web member can be converted to the node plate, so as to facilitate formula derivation. The specific process is as follows:
as shown in fig. 5, DB ≠ AB, a point P is selected on AB, AD is h, and angle BDP is βyThe following can be obtained:
Figure BDA0003120078300000093
then further L can be obtainedDP(βy) With respect to betayThe derivative function of (d) is:
Figure BDA0003120078300000094
βythe value range is [0,0.5 pi-alphay]When sin betay＜ηcosαyWhen L isDP(βy) With respect to betayMonotonically decreasing when sin betay>ηcosαyWhen L isDP(βy) With respect to betayMonotonically increasing. In sin betay＝ηcosαyWhen L isDP(βy) Taking a minimum value of
Figure BDA0003120078300000101
Based on LDP(βy) The minimum value of (a) defines the horizontal plate coefficient of the web member as:
Figure BDA0003120078300000102
wherein, deltayIs the horizontal plate thickness of the web member, delta0Is the gusset plate thickness.
Therefore, converting the web horizontal panel tear path length to the equivalent length on the gusset panel can be expressed as:
Lequivalent DPH Λ, where Λ is the web horizontal plate coefficient, which is typically between 0.2 and 0.45.
In actual calculation, the web members can be classified according to the web members at the nodes and the characteristics of the nodes, and the horizontal plate coefficient and the tearing path length of each web member are calculated.
In some embodiments, as shown in fig. 6, the web member is a web member with an H-shaped section, and the two sides of the web member riser are symmetrical bevel edges; taking this as the first condition, step S400 includes the steps of: calculating a tearing path corresponding to the web member according to a first formula;
the first formula is:
Figure BDA0003120078300000103
wherein L is1、L2And L3The smaller value in (A) is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the height of the web member vertical plate, H is the projection length of the intersection point of the web member vertical plate symmetrical bevel edge and the web member vertical plate to the end distance in the web member horizontal plate node on the web member axis, and Λ is the coefficient of the web member horizontal plate, alphafIs the included angle between the bevel edge of the web member vertical plate and the axis of the web member.
As shown in fig. 7, in some embodiments, the web member is an H-section web member, and the two sides of the web member riser are circular arc edges; taking this as the second operating condition, step S400 includes the steps of: calculating a tearing path corresponding to the web member according to a second formula;
the second formula is:
Figure BDA0003120078300000111
wherein L is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the height of the web member vertical plate, and R is1And R2Are respectively the arc radii of two sides of the web member vertical plate H1And H2The projection lengths of the distances from arc starting points of arc edges on two sides of the web member vertical plate to the inner end part of the web member horizontal plate gusset plate on the axis of the web member are respectively, and the lambada is the coefficient of the web member horizontal plate.
As shown in fig. 8, in some embodiments the web member is a box section web member with web risers flanked by symmetrically beveled edges; taking this as the third condition, step S400 includes the steps of: calculating a tearing path corresponding to the web member according to a third formula;
the third formula is:
Figure BDA0003120078300000112
wherein L is1、L2And L3The smaller value in the height-adjustable net distance is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, D is the sum of the distances from the inner sides of the upper horizontal plate and the lower horizontal plate of the web member to the edge of the vertical plate, H is the projection length of the distance from the symmetrical bevel edge of the web member vertical plate and the intersection point of the web member vertical plate to the inner end part of the web member horizontal plate node on the axis of the web member, D is the net distance of the upper horizontal plate and the lower horizontal plate of the web member, Λ is the coefficient of the web member horizontal plate, and alpha is the net distance of the web member horizontal platefIs the included angle between the bevel edge of the web member vertical plate and the axis of the web member.
In some embodiments, as shown in fig. 9, the web member is a box section web member, and the vertical plate of the web member is provided with symmetrical circular arc edges at two sides; with this as the fourth condition, the step S400 includes the steps of: calculating a tearing path corresponding to the web member according to a fourth formula;
the fourth formula is:
Figure BDA0003120078300000121
l is the shortest tearing path length of converting the web member horizontal plate to the gusset plate, D is the sum of distances from the inner sides of the upper and lower horizontal plates of the web member to the edge of the vertical plate, R is the arc radius of the two sides of the web member vertical plate, H is the projection length of the arc starting point of the arc edge of the web member vertical plate to the distance from the inner end part of the gusset plate of the web member horizontal plate on the axis of the web member, D is the net distance of the upper and lower horizontal plates of the web member, and Lambda is the coefficient of the web member horizontal plate.
As shown in fig. 10, in some embodiments, the web member is a web member with an H-shaped cross section, and the two sides of the web member riser are asymmetric circular arc edges; taking this as the fifth operating condition, step S400 includes the steps of: calculating a tearing path corresponding to the web member according to a fifth formula;
the fifth formula is:
Figure BDA0003120078300000122
wherein, L (h)1,h2) The minimum value of (A) is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the sum of the distances from the inner sides of the upper and lower horizontal plates of the web member to the edge of the vertical plate, R1And R2Are respectively the arc radii of two sides of the web member vertical plate H1The vertical plate radius of the web member is R1The projection length of the distance from the arc starting point of the arc edge to the inner end part of the node plate of the horizontal plate of the web member on the same side on the axis of the web member, H2The vertical plate radius of the web member is R2The projection length of the distance from the arc starting point of the arc edge to the inner end part of the node plate of the horizontal plate of the web member on the same side on the axis of the web member, H0The projection distance of the inner end parts of the upper horizontal plate node plate and the lower horizontal plate node plate of the web member on the axis of the web member, D is the net distance of the upper horizontal plate and the lower horizontal plate of the web member, Lambda is the coefficient of the horizontal plate of the web member, h1And h2Is a variable, LhThe (h, R) function is LβThe (beta) function being [0,0.5 pi ] with respect to beta]Defining a minimum value within the domain;
the function LβThe formula for the calculation of (. beta.) is:
Figure BDA0003120078300000131
wherein beta is a value within [0,0.5 pi ].
Preferably, the grid method is adopted to pair L (h)1，h2) And carrying out numerical calculation, wherein the calculation steps are as follows:
s1, pair h1And h2Carrying out grid division in the definition domain, wherein the grid node coordinate is [ h ]1(i)，h2(j)]；
S2, substituting each node in S1 into a function LβThe calculation formula of (beta) is used for carrying out numerical calculation, and the numerical calculation step is as follows:
s2a, carrying out grid division on the beta, wherein the grid node coordinate is beta (k);
s2b, aiming at the node [ h ] in S11(i)，h2(j)]Calculate all Lβ[β(k)]；
S2c to obtain Lβ[β(k)]And back to the fifth formula.
S3, calculating all L h1(i)，h2(j)]To obtain L [ h ]1(i)，h2(j)]Is the shortest tear path length.
It should be noted that, since the number of mesh divisions has a certain influence on the calculation result, according to the example calculation, when the number of mesh divisions N is 100, the path length calculation accuracy can be within 1%, and therefore, it is preferable to set the number of mesh divisions to 100, and thus, it is possible to obtain:
Figure BDA0003120078300000132
further, the mesh of β may be divided into 100 parts in step S2a so that the calculation accuracy is within 1%, whereby:
Figure BDA0003120078300000133
wherein M is 100.
Step S2b requires each node [ h ] of input1(i)，h2(j)]All L's are calculatedβ[β(k)]And k is 1 to M. Therefore every time a web member is calculated MN needs to be calculated2And the calculation amount is large. In order to reduce the calculation amount, the values of N and M should not be too large. In the actual calculation, an appropriate value may be calculated by trial based on actual engineering.
In the description of the present invention, it should be noted that the terms "upper", "lower", and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, which are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and operate, and thus, should not be construed as limiting the present invention. Unless expressly stated or limited otherwise, the terms "mounted," "connected," and "connected" are intended to be inclusive and mean, for example, that they may be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
It is to be noted that, in the present invention, relational terms such as "first" and "second", and the like, are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The foregoing are merely exemplary embodiments of the present invention, which enable those skilled in the art to understand or practice the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. The method for calculating the tearing path of the all-welded integral node based on the fitting Mises yield criterion is characterized by comprising the following steps of:
defining theoretical equivalent allowable stress based on Mises yield criterion so that the theoretical equivalent allowable stress considers normal stress and shear stress on a diagonal line;
fitting the theoretical equivalent allowable stress to obtain a fitted equivalent allowable stress;
defining a web member horizontal plate coefficient based on the fitted equivalent allowable stress;
and calculating the tearing path corresponding to the web member based on the horizontal plate coefficient of the web member.
2. The method of claim 1 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
defining a theoretical equivalent allowable stress based on the Mises yield criterion so that the theoretical equivalent allowable stress considers normal stress and shear stress on a diagonal line, comprising the steps of:
acquiring normal stress and shear stress on the oblique line;
the calculation formula of the normal stress on the oblique line is as follows:
Figure FDA0003120078290000011
the calculation formula of the shear stress on the oblique line is as follows:
Figure FDA0003120078290000012
wherein, sigma is the positive stress on the oblique line, tau is the shearing stress on the oblique line, delta is the structure thickness, T is the tension, alphaxThe included angle between the tearing path and the perpendicular line of the stress direction is shown, and l is the length of the oblique line;
and converting the normal stress and the shear stress on the oblique line into equivalent allowable stress on the oblique line according to the Mises yield criterion.
3. The method of claim 2 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
converting the normal stress and the shear stress on the oblique line into equivalent allowable stress on the oblique line according to Mises yield criterion, and the method comprises the following steps:
obtaining a conversion stress calculation formula on the oblique line according to the Mises yield criterion;
the calculation formula of the converted stress on the oblique line is as follows:
Figure FDA0003120078290000021
defining a theoretical equivalent allowable stress based on a conversion stress calculation formula on the oblique line;
the calculation formula of the theoretical equivalent allowable stress is as follows:
Figure FDA0003120078290000022
wherein the content of the first and second substances,
[σ]0xfor theoretical equivalent allowable stress, [ sigma ]]The material is substantially stress tolerant.
4. The method of claim 3 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
fitting the theoretical equivalent allowable stress to obtain a fitted equivalent allowable stress coefficient, comprising the steps of:
carrying out linear fitting processing on the calculation formula of the theoretical equivalent allowable stress under the same boundary condition to obtain fitted equivalent allowable stress;
the calculation formula of the fitting equivalent allowable stress is as follows:
[σ]x＝(1-ηsinαx)[σ]
Figure FDA0003120078290000023
where η is the fitting coefficient.
5. The method of claim 4 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
the calculation formula of the horizontal plate coefficient of the web member is as follows:
Figure FDA0003120078290000024
wherein, deltayIs the web member horizontal plate thickness, alphayFor web member horizontal plate dovetail plate corner cut, RyFor rounding the web-member horizontal-plate dovetail-plate with an arc radius, delta0Is the gusset plate thickness.
6. The method of claim 5 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
the web member is an H-shaped section web member, and two sides of a vertical plate of the web member are symmetrical bevel edges;
calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of:
calculating a tearing path corresponding to the web member according to a first formula;
the first formula is:
Figure FDA0003120078290000031
wherein L is1、L2And L3The smaller value in (A) is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the height of the web member vertical plate, H is the projection length of the intersection point of the web member vertical plate symmetrical bevel edge and the web member vertical plate to the end distance in the web member horizontal plate node on the web member axis, and Λ is the coefficient of the web member horizontal plate, alphafIs the included angle between the bevel edge of the web member vertical plate and the axis of the web member.
7. The method of claim 5 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
the web members are H-shaped cross-section web members, and arc edges are arranged on two sides of vertical plates of the web members;
calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of:
calculating a tearing path corresponding to the web member according to a second formula;
the second formula is:
Figure FDA0003120078290000032
wherein L is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the height of the web member vertical plate, and R is1And R2Are respectively the arc radii of two sides of the web member vertical plate H1And H2The projection lengths of the distances from arc starting points of arc edges on two sides of the web member vertical plate to the inner end part of the web member horizontal plate gusset plate on the axis of the web member are respectively, and the lambada is the coefficient of the web member horizontal plate.
8. The method of claim 5 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
the web member is a box-shaped section web member, and two sides of a vertical plate of the web member are symmetrical bevel edges;
calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of:
calculating a tearing path corresponding to the web member according to a third formula;
the third formula is:
Figure FDA0003120078290000041
wherein L is1、L2And L3The smaller value is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the sum of the distances from the inner sides of the upper and lower horizontal plates of the web member to the edge of the vertical plate, and H is the symmetrical bevel edge of the vertical plate of the web memberThe projection length of the distance from the intersection point of the vertical plate of the web member to the inner end part of the horizontal plate node of the web member on the axis of the web member, D is the net distance between the upper horizontal plate and the lower horizontal plate of the web member, Lambda is the coefficient of the horizontal plate of the web member, alphafIs the included angle between the bevel edge of the web member vertical plate and the axis of the web member.
9. The method of claim 5 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
the web members are box-shaped section web members, and two sides of vertical plates of the web members are symmetrical arc edges;
calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of:
calculating a tearing path corresponding to the web member according to a fourth formula;
the fourth formula is:
Figure FDA0003120078290000042
l is the shortest tearing path length of converting the web member horizontal plate to the gusset plate, D is the sum of distances from the inner sides of the upper and lower horizontal plates of the web member to the edge of the vertical plate, R is the arc radius of the two sides of the web member vertical plate, H is the projection length of the arc starting point of the arc edge of the web member vertical plate to the distance from the inner end part of the gusset plate of the web member horizontal plate on the axis of the web member, D is the net distance of the upper and lower horizontal plates of the web member, and Lambda is the coefficient of the web member horizontal plate.
10. The method of claim 5 for computing an all-welded monolithic node tear path based on fitting Mises yield criteria,
the web members are H-shaped cross-section web members, and two sides of vertical plates of the web members are asymmetric arc edges;
calculating a tearing path corresponding to the web member based on the horizontal plate coefficient of the web member, comprising the steps of:
calculating a tearing path corresponding to the web member according to a fifth formula;
the fifth formula is:
Figure FDA0003120078290000051
wherein, L (h)1,h2) The minimum value of (A) is the shortest tearing path length converted from the web member horizontal plate to the gusset plate, d is the sum of the distances from the inner sides of the upper and lower horizontal plates of the web member to the edge of the vertical plate, R1And R2Are respectively the arc radii of two sides of the web member vertical plate H1The vertical plate radius of the web member is R1The projection length of the distance from the arc starting point of the arc edge to the inner end part of the node plate of the horizontal plate of the web member on the same side on the axis of the web member, H2The vertical plate radius of the web member is R2The projection length of the distance from the arc starting point of the arc edge to the inner end part of the node plate of the horizontal plate of the web member on the same side on the axis of the web member, H0The projection distance of the inner end parts of the upper horizontal plate node plate and the lower horizontal plate node plate of the web member on the axis of the web member, D is the net distance of the upper horizontal plate and the lower horizontal plate of the web member, Lambda is the coefficient of the horizontal plate of the web member, h1And h2Is a variable, LhThe (h, R) function is LβThe (beta) function being [0,0.5 pi ] with respect to beta]Defining a minimum value within the domain;
the function LβThe formula for the calculation of (. beta.) is:
Figure FDA0003120078290000052
wherein beta is a value within [0,0.5 pi ].
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090177417A1 (en) * 2006-02-01 2009-07-09 Shigeru Yonemura Fracture prediction method, device, a program arrangement and computer-accessible medium therefor
JP2013145529A (en) * 2012-01-16 2013-07-25 Lixil Corp Calculation method of allowable shearing proof stress of bearing wall having aperture, design method of bearing wall having aperture, arithmetic unit of allowable shearing proof stress of bearing wall having aperture, and calculation program of allowable shearing proof stress of bearing wall having aperture
CN111090904A (en) * 2019-12-23 2020-05-01 辽宁工程技术大学 Soil pressure calculation method based on generalized double-shear stress yield criterion
CN112699448A (en) * 2021-01-13 2021-04-23 中铁大桥勘测设计院集团有限公司 Calculation method for tearing of integral node of all-welded steel truss girder

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20090177417A1 (en) * 2006-02-01 2009-07-09 Shigeru Yonemura Fracture prediction method, device, a program arrangement and computer-accessible medium therefor
JP2013145529A (en) * 2012-01-16 2013-07-25 Lixil Corp Calculation method of allowable shearing proof stress of bearing wall having aperture, design method of bearing wall having aperture, arithmetic unit of allowable shearing proof stress of bearing wall having aperture, and calculation program of allowable shearing proof stress of bearing wall having aperture
CN111090904A (en) * 2019-12-23 2020-05-01 辽宁工程技术大学 Soil pressure calculation method based on generalized double-shear stress yield criterion
CN112699448A (en) * 2021-01-13 2021-04-23 中铁大桥勘测设计院集团有限公司 Calculation method for tearing of integral node of all-welded steel truss girder

Non-Patent Citations (11)

* Cited by examiner, † Cited by third party
Title
E.ØSTBYA 等: "Numerical simulations of specimen size and mismatch effects in ductile crack growth – Part I: Tearing resistance and crack growth paths", 《ENGINEERING FRACTURE MECHANICS》 *
何东升等: "板桁组合结构主桁节点板应力集中系数研究", 《桥梁建设》 *
康晋等: "平潭海峡公铁两用大桥主桥整节段全焊钢桁梁设计", 《桥梁建设》 *
张燕等: "不同构造的钢-混凝土组合桁架节点受力性能试验研究", 《建筑结构学报》 *
李燕军: "钢桁梁节点板的抗撕破计算分析", 《山西建筑》 *
杨强等: "基于二阶组构张量的各向异性屈服准则", 《工程力学》 *
柳晓晨等: "铝合金网壳结构盘式节点承载力计算方法研究", 《建筑结构》 *
董石麟等: "轴力和弯矩共同作用下焊接空心球节点承载力研究与实用计算方法", 《土木工程学报》 *
郭彦林等: "波浪腹板钢结构设计理论研究及应用现状", 《工业建筑》 *
钟演材: "钢结构连接节点处板件的计算研究", 《建材与装饰(中旬刊)》 *
闫兴非: "钢桁梁整体焊接节点试验与非线性有限元分析", 《公路交通科技(应用技术版)》 *

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