CN113239431A - Method for calculating ultimate strength of thin-walled beam under shear-torsion combined load action - Google Patents
Method for calculating ultimate strength of thin-walled beam under shear-torsion combined load action Download PDFInfo
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Abstract
A method for calculating the ultimate strength of a thin-wall beam under the action of shear-torsion combined load comprises the following steps: s1, dispersing the thin-wall beam section into a grid unit, establishing a thin-wall beam section single span calculation model, and inputting basic material attributes; step S2, applying shearing force, and calculating the shearing stress of the vertical plate grids and the shearing stress of each horizontal plate grid in the cross section; step S3, calculating the limit shear stress of the plate grid; step S4, constructing a relation curve of the shear stress and the shear strain in the torsion process according to the calculated torsion limit shear stress and the width-thickness ratio of each plate lattice; and step S5, applying a torsion angle to the thin-wall beam, calculating the shear strain of each plate lattice, calculating the shear stress of the plate lattices according to the shear stress-strain relationship, summing the contribution of each plate lattice to the torque to obtain the torque, increasing the torsion angle to perform iterative calculation, and taking the maximum value of the torque in the iterative process as the limit torque considering the shearing force action. The method is simple, accurate and efficient in calculation.
Description
Technical Field
The invention relates to the field of thin-wall beam structure design, and provides a method for calculating the ultimate strength of a thin-wall beam under the action of shear-torsion combined load aiming at a beam section with smaller double moment, so that the ultimate strength of the thin-wall beam under the action of different shear-torsion load combinations can be quickly calculated, and the structure can be designed and optimized according to the calculation result.
Background
At present, the ultimate strength of the thin-wall beam is researched mainly aiming at single load, and research under combined load is very rare, however, in actual working conditions, the thin-wall beam is easily subjected to multiple actions of wind, sea waves, load and the like, and is not under the action of single load. Especially for container ships, due to the characteristics of cargo loading, large openings are formed in the deck, so that the torsional strength is low. Therefore, the analysis of the ultimate strength under the shear-torsion combined load is very important.
At present, a finite element method is mainly adopted for calculating the ultimate bearing capacity of the thin-wall beam under the shearing and twisting combined load effect, a large amount of time is needed for establishing a fine model and nonlinear solution, time and labor are wasted, and the requirement on a calculator is high, so that the industry needs to find a method for calculating the ultimate strength of the thin-wall beam under the shearing and twisting combined load effect, which is simple, accurate and efficient in calculation aiming at a beam section with small double moment.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the thin-wall beam ultimate strength calculation method under the action of the shear-torsion combined load, which is simple, accurate and efficient in calculation.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for calculating the ultimate strength of a thin-wall beam under the action of shear-torsion combined load comprises the following steps:
step S1, dispersing the thin-wall beam section into a plate grid unit according to the positions of the stiffening material and the longitudinal bone in the section, establishing a thin-wall beam section single span calculation model, and inputting basic material attributes, wherein the basic material attributes comprise section material yield strength, elastic modulus and Poisson ratio;
step S2, applying shearing force, summing the cross section area sum of the vertical component of the thin-wall beam section, neglecting the shearing resistance and torsion resistance of the aggregate component, calculating the shearing stress of the vertical plate lattice, and calculating the shearing stress of each horizontal plate lattice in the section according to the shear flow distribution assumption of the limit state under the pure shearing action;
step S3, calculating the limit shear stress of the plate lattice, substituting the shear stress of the plate lattice into a stress equation of the limit state of the plate lattice, and calculating to obtain the torsional limit shear stress after considering the shearing force;
step S4, calculating the width-thickness ratio of each plate lattice according to the calculated torsion limit shear stress, and constructing a relation curve of the shear stress and the shear strain in the torsion process;
and step S5, applying a torsion angle to the thin-wall beam, calculating the shear strain of each plate lattice, calculating the shear stress of the plate lattices according to the shear stress-strain relationship, summing the contribution of each plate lattice to the torque to obtain the torque, increasing the torsion angle to perform iterative calculation, and taking the maximum value of the torque in the iterative process as the limit torque considering the shearing force action.
Further, in step S2, the calculation formula of the total area of the vertical plate grid cells is as follows:
wherein n is the total number of panels, liThe width of the ith plate grid is mm; t is tiThe thickness of the ith plate grid is mm; sin thetaiThe included angle between the ith plate grid and the horizontal line is set;
the shear stress of the vertical plate grid is as follows:
f is applied shearing force, and in addition, due to the circulation effect of the shearing flow, shearing stress exists in the horizontal plate grid of the thin-wall beam; and calculating the shear stress of the horizontal plate grids according to the shear flow distribution rule of the thin-wall beam under the pure shearing action and by combining the shear stress of the vertical plate grids.
Still further, in the step S3, the shear stress τ is limited for the simply-supported four-sided board gridCThe calculation formula is as follows:
wherein, tauCThe ultimate shear strength of the panel; reH-PIs the yield strength of the material of the plate grid, N/mm2；CτAs a flexion reduction factor, there are:
λ is the reference slenderness ratio of the plate grid, and has:
k is the buckling factor, which is:
σEreference stress for the plate grid, N/mm2；
Wherein E is the elastic modulus of the material, N/mm2(ii) a t is the net thickness of the plate lattice, mm; a. b is the length and width of the plate grid respectively, mm;
according to the obtained shear stress under the shearing force action and the plate grid limit shear stress, the torsional limit shear stress after the shearing force action is calculated, and the calculation formula is as follows:
τcr＝τC-τs
wherein, taucrTo take into account the ultimate shear stress after shear action, N/mm2；τCIs the ultimate shear stress of the plate grid, N/mm2；τsIs the shear stress of the plate lattice under the action of shearing force, N/mm2。
In step S4, β is the width-to-thickness ratio of the plate, and the calculation formula is:
wherein b is the width of the plate grid in mm2T is the net thickness of the plate grid, mm2E is the elastic modulus of the material, N/mm2，ReH-pIs the material yield strength of the plate lattice, N/mm2；
According to the property of the width-thickness ratio of the plate, the curve relation of the shear stress and the shear strain in the plate lattice torsion process is constructed as follows:
wherein, γEIs unit strain, gammayThe strain at which the cell yields is determined by the following equation:
wherein R iseH-PIs the yield strength of the material of the plate grid, N/mm2And G is shear modulus.
In the step S5, an initial torsion angle is given to the thin-wall beam, the strain of each plate lattice at the initial torsion angle is calculated according to the distance between the plate lattice and the centroid of the cross section, the shear stress of each plate lattice is calculated according to the relation between the shear stress and the shear strain, the shear stress of each plate lattice is obtained by multiplying the area of the plate lattice, the moment is obtained by multiplying the distance between the plate lattice and the centroid of the cross section, and the moment of all the plate lattices is accumulated to obtain the torque of the section constraint torsion of the thin-wall beam at the initial torsion angle.
The invention has the following beneficial effects: the method is applied to calculating the ultimate bearing capacity of the thin-wall beam under the action of shear-torsion combined load. And checking the two real containers, analyzing and comparing the formula calculation value and the finite element calculation value, and finding that the difference between the formula calculation value and the finite element simulation result is small, and the formula calculation has high precision.
The method can quickly and accurately calculate the limit bearing capacity of the thin-wall beam for restraining and twisting.
Drawings
FIG. 1 is a flow chart of a method for calculating ultimate strength of a thin-wall beam under the action of shear-torsion combined load.
FIG. 2 is a schematic diagram of unit division of a thin-wall beam section under the action of shearing force and torsion.
FIG. 3 is a shear distribution diagram of a thin wall beam under pure shear, wherein (a) the shear distribution at the side wall is assumed; (b) double-layer bottom shear flow distribution hypothetical graph.
FIG. 4 is a flow chart of the calculation of the ultimate strength of the thin-wall beam under the action of shear-torsion combined load.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 4, a method for calculating ultimate strength of a thin-walled beam under the action of shear-torsion combined load comprises the following steps:
step S1, dispersing the thin-wall beam section into a plate grid unit according to the positions of the stiffening material and the longitudinal bone in the section, establishing a thin-wall beam section single span calculation model, and inputting basic material attributes, wherein the basic material attributes comprise section material yield strength, elastic modulus and Poisson ratio;
step S2, applying shearing force, summing the cross section area sum of the vertical component of the thin-wall beam section, neglecting the shearing resistance and torsion resistance of the aggregate component, calculating the shearing stress of the vertical plate lattice, and calculating the shearing stress of each horizontal plate lattice in the section according to the shear flow distribution assumption of the limit state under the pure shearing action;
step S3, calculating the limit shear stress of the plate lattice, substituting the shear stress of the plate lattice into a stress equation of the limit state of the plate lattice, and calculating to obtain the torsional limit shear stress after considering the shearing force;
step S4, calculating the width-thickness ratio of each plate lattice according to the calculated torsion limit shear stress, and constructing a relation curve of the shear stress and the shear strain in the torsion process;
and step S5, applying a torsion angle to the thin-wall beam, calculating the shear strain of each plate lattice, calculating the shear stress of the plate lattices according to the shear stress-strain relationship, summing the contribution of each plate lattice to the torque to obtain the torque, increasing the torsion angle to perform iterative calculation, and taking the maximum value of the torque in the iterative process as the limit torque considering the shearing force action.
In the step S2, a shearing force is applied, the sum of the cross-sectional areas of the vertical members in the section of the thin-walled beam is summed, the shearing resistance and the torsion resistance of the members such as the aggregate are neglected, the shearing stress of the vertical plate lattice is calculated, and the shearing stress of each horizontal plate lattice in the section is calculated according to the assumption of the shear flow distribution in the limit state under the pure shearing action. The calculation formula of the total area of the vertical plate grid cells is as follows:
wherein n is the total number of panels, liThe width of the ith plate grid is mm; t is tiThe thickness of the ith plate grid is mm; sin thetaiThe included angle between the ith plate grid and the horizontal line is shown.
The shear stress of the vertical plate grid is as follows:
f is applied shear force, and in addition, due to the circulation effect of shear flow, a certain shear stress exists in the horizontal plate grid of the thin-wall beam, and the distribution rule of the shear stress is shown in fig. 2.
And calculating the shear stress of the horizontal plate grids according to the shear flow distribution rule of the thin-wall beam under the pure shearing action and by combining the shear stress of the vertical plate grids.
In the step S3, the ultimate shear stress of the plate lattice is calculated, the shear stress of the plate lattice is introduced into the ultimate state stress equation of the plate lattice, and the torsional ultimate shear stress after the shearing force action is considered is calculated.
Ultimate shear stress force tau for simply supported four-side plate gridsCThe specific calculation formula is as follows:
wherein, tauCThe ultimate shear strength of the panel; reH-pIs the yield strength of the material of the plate grid, N/mm2；CτAs a flexion reduction factor, there are:
λ is the reference slenderness ratio of the plate grid, and has:
k is the buckling factor, which is:
σEreference stress for the plate grid, N/mm2；
Wherein E is the elastic modulus of the material, N/mm2(ii) a t is the net thickness of the plate lattice, mm; a. b is the length and width of the plate grid respectively, mm.
According to the obtained shear stress under the shearing force action and the plate grid limit shear stress, the torsional limit shear stress after the shearing force action is calculated, and the calculation formula is as follows:
τcr＝τC-τs
wherein, taucrTo take into account the ultimate shear stress after shear action, N/mm2；τCIs the ultimate shear stress of the plate grid, N/mm2；τsIs the shear stress of the plate lattice under the action of shearing force, N/mm2。
In the step S4, the width-to-thickness ratio of each plate lattice is calculated according to the calculated torsion limit shear stress, and a relationship curve between the shear stress and the shear strain in the torsion process is constructed;
beta is the width-thickness ratio of the plate, and the calculation formula is as follows:
wherein b is the width of the plate grid in mm2T is the net thickness of the plate grid, mm2E is the elastic modulus of the material, N/mm2，ReH-pIs the yield strength of the material of the plate grid, N/mm2；
According to the property of the width-thickness ratio of the plate, the curve relation of the shear stress and the shear strain in the plate lattice torsion process is constructed as follows:
in the formula, gammaEIs unit strain, gammayThe strain at which the cell yields is determined by the following equation:
wherein R iseH-PIs the yield strength of the material of the plate grid, N/mm2And G is shear modulus.
In the step S5, an initial torsion angle is given to the thin-wall beam, the strain of each plate lattice at the initial torsion angle is calculated according to the distance between the plate lattice and the centroid of the cross section, the shear stress of each plate lattice is calculated according to the relation between the shear stress and the shear strain, the shear stress of each plate lattice is obtained by multiplying the area of the plate lattice, the moment is obtained by multiplying the distance between the plate lattice and the centroid of the cross section, and the moment of all the plate lattices is accumulated to obtain the torque of the section constraint torsion of the thin-wall beam at the initial torsion angle.
And (3) calculating the moment of the plate lattices to the cross section core according to the known shearing force of the plate lattices at the initial torsion angle, and accumulating the moments of all the plate lattices to obtain the torsion restraining torque of the section of the thin-wall beam at the initial torsion angle. The specific calculation flowchart is shown in fig. 4.
To verify the accuracy of the proposed method, two container ships and ocean platform were checked and compared with finite elements, and table 1 is the shear-torsion combination ultimate strength comparison (shear 10) for container ship No. 18N, torque 1013N·mm)。
TABLE 1
Table 2 shows the ultimate strength comparison (shear 10) of the shear-torsion combination of No. 2 container ship8N, torque 1013N·mm)。
TABLE 2
The embodiments described in this specification are merely illustrative of implementations of the inventive concepts, which are intended for purposes of illustration only. The scope of the present invention should not be construed as being limited to the particular forms set forth in the examples, but rather as being defined by the claims and the equivalents thereof which can occur to those skilled in the art upon consideration of the present inventive concept.
Claims (5)
1. A method for calculating the ultimate strength of a thin-wall beam under the action of shear-torsion combined load is characterized by comprising the following steps:
step S1, dispersing the thin-wall beam section into a plate grid unit according to the positions of the stiffening material and the longitudinal bone in the section, establishing a thin-wall beam section single span calculation model, and inputting basic material attributes, wherein the basic material attributes comprise section material yield strength, elastic modulus and Poisson ratio;
step S2, applying shearing force, summing the cross section area sum of the vertical component of the thin-wall beam section, neglecting the shearing resistance and torsion resistance of the aggregate component, calculating the shearing stress of the vertical plate lattice, and calculating the shearing stress of each horizontal plate lattice in the section according to the shear flow distribution assumption of the limit state under the pure shearing action;
step S3, calculating the limit shear stress of the plate lattice, substituting the shear stress of the plate lattice into a stress equation of the limit state of the plate lattice, and calculating to obtain the torsional limit shear stress after considering the shearing force;
step S4, calculating the width-thickness ratio of each plate lattice according to the calculated torsion limit shear stress, and constructing a relation curve of the shear stress and the shear strain in the torsion process;
and step S5, applying a torsion angle to the thin-wall beam, calculating the shear strain of each plate lattice, calculating the shear stress of the plate lattices according to the shear stress-strain relationship, summing the contribution of each plate lattice to the torque to obtain the torque, increasing the torsion angle to perform iterative calculation, and taking the maximum value of the torque in the iterative process as the limit torque considering the shearing force action.
2. The method for calculating the ultimate strength of a thin-walled beam under the action of a shear-torsion combined load according to claim 1, wherein in the step S2, the calculation formula of the total area of the vertical plate grid cells is as follows:
wherein n is the total number of panels, liThe width of the ith plate grid is mm; t is tiThe thickness of the ith plate grid is mm; sin thetaiThe included angle between the ith plate grid and the horizontal line is set;
the shear stress of the vertical plate grid is as follows:
f is applied shearing force, and in addition, due to the circulation effect of the shearing flow, shearing stress exists in the horizontal plate grid of the thin-wall beam; and calculating the shear stress of the horizontal plate grids according to the shear flow distribution rule of the thin-wall beam under the pure shearing action and by combining the shear stress of the vertical plate grids.
3. The method for calculating the ultimate strength of the thin-wall beam under the action of the shear-torsion combined load according to claim 1 or 2, wherein in the step S3, the ultimate shear stress tau of the four-side simply-supported plate grids is calculatedCThe calculation formula is as follows:
wherein, tauCThe ultimate shear strength of the panel; reH-PIs the yield strength of the material of the plate grid, N/mm2；
CτAs a flexion reduction factor, there are:
λ is the reference slenderness ratio of the plate grid, and has:
k is the buckling factor, which is:
σEreference stress for the plate grid, N/mm2；
Wherein E is the elastic modulus of the material, N/mm2(ii) a t is the net thickness of the plate lattice, mm; a. b is the length and width of the plate grid respectively, mm;
according to the obtained shear stress under the shearing force action and the plate grid limit shear stress, the torsional limit shear stress after the shearing force action is calculated, and the calculation formula is as follows:
τcr＝τC-τs
wherein, taucrTo take into account the ultimate shear stress after shear action, N/mm2；τCIs a plate grid limitShear stress, N/mm2；τsIs the shear stress of the plate lattice under the action of shearing force, N/mm2。
4. The method for calculating the ultimate strength of the thin-wall beam under the action of the shear-torsion combined load according to claim 1 or 2, wherein in the step S4, β is the width-thickness ratio of the plate, and the calculation formula is as follows:
wherein b is the width of the plate grid in mm2T is the net thickness of the plate grid, mm2E is the elastic modulus of the material, N/mm2，ReH-PIs the yield strength of the material of the plate grid, N/mm2；
According to the property of the width-thickness ratio of the plate, the curve relation of the shear stress and the shear strain in the plate lattice torsion process is constructed as follows:
wherein, γEIs unit strain, gammayThe strain at which the cell yields is determined by the following equation:
wherein R iseH-PIs the yield strength of the material of the plate grid, N/mm2And G is shear modulus.
5. A thin-wall beam ultimate strength calculation method under the action of shear-torsion combined load according to claim 1 or 2, characterized in that in step S5, an initial torsion angle is given to the thin-wall beam, the strain of each plate lattice under the initial torsion angle is calculated according to the distance between the plate lattice and the centroid of the cross section, the shear stress of each plate lattice is calculated according to the relation between the shear stress and the shear strain, the shear stress of each plate lattice is obtained by multiplying the area of the plate lattice, the moment is obtained by multiplying the distance between the plate lattice and the centroid of the cross section, and the moments of all the plate lattices are accumulated to obtain the torsion restraining torque of the thin-wall beam cross section under the initial torsion angle.
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