CN113239431B - Method for calculating ultimate strength of thin-wall beam under shearing and twisting combined load action - Google Patents

Method for calculating ultimate strength of thin-wall beam under shearing and twisting combined load action Download PDF

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CN113239431B
CN113239431B CN202110483775.9A CN202110483775A CN113239431B CN 113239431 B CN113239431 B CN 113239431B CN 202110483775 A CN202110483775 A CN 202110483775A CN 113239431 B CN113239431 B CN 113239431B
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吴剑国
李钧晖
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Zhejiang University of Technology ZJUT
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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 a thin-wall beam section into lattice units, establishing a thin-wall beam section single-span calculation model, and inputting basic material properties; s2, applying shearing force, and calculating the shearing stress of the vertical plate panels and the shearing stress of each horizontal plate panel in the section; s3, calculating limit shear stress of the plate grid; 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-to-thickness ratio of each plate grid; and S5, applying a torsion angle to the thin-wall beam, calculating the shear strain of each plate grid, calculating the shear stress of each plate grid according to the shear stress-strain relation, calculating the contribution of each plate grid to the torque to obtain the torque, increasing the torsion angle, and performing iterative calculation, wherein the maximum value of the torque in the iterative process is used as the limit torque after the shearing force is considered. The invention has simple, accurate and efficient calculation.

Description

Method for calculating ultimate strength of thin-wall beam under shearing and twisting combined load action
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 combined shearing and twisting load action aiming at a beam section with smaller double moment.
Background
The ultimate strength research of the thin-wall beam is mainly aimed at single load, and the research under combined load is quite rare, however, in actual working conditions, the thin-wall beam is easy to be subjected to multiple actions such as wind, sea wave and load, and the like, and the thin-wall beam is not subjected to the action of single load. Particularly for container ships, the large opening of the deck is created due to the nature of the cargo, which results in less torsional strength. Therefore, it is important to analyze the ultimate strength of the shear-torsion combination under the action of the load.
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 action, a great amount of time is required to build a fine model and carry out nonlinear solution, time and labor are wasted, and the requirement on calculation staff is high, so that the industry needs to search for a method for calculating the ultimate strength of the thin-wall beam under the shearing and twisting combined load action, which aims at a beam section with smaller double moment, and is simple, accurate and efficient in calculation.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for calculating the ultimate strength of the thin-wall beam under the action of shear-torsion combined load, which is simple, accurate and efficient in calculation.
The technical scheme adopted 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:
S1, dispersing a thin-wall beam section into lattice units according to positions of strengthening materials and longitudinal bones in the section, establishing a thin-wall beam section single-span calculation model, and inputting basic material properties, wherein the basic material properties comprise yield strength, elastic modulus and Poisson' S ratio of the section material;
S2, applying shearing force, adding up the sum of the cross-sectional areas of the vertical members of the thin-wall beam section, neglecting the shearing resistance and torsion resistance of the aggregate members, calculating the shearing stress of the vertical plate panels, and calculating the shearing stress of each horizontal plate panel in the section according to the shearing flow distribution assumption of the limit state under the pure shearing action;
S3, calculating the limit shear stress of the plate, bringing the shear stress of the plate into a limit state stress equation of the plate, and calculating to obtain the torsional limit shear stress taking the shear effect into consideration;
S4, calculating the width-to-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 S5, applying a torsion angle to the thin-wall beam, calculating the shear strain of each plate grid, calculating the shear stress of each plate grid according to the shear stress-strain relation, calculating the contribution of each plate grid to the torque to obtain the torque, increasing the torsion angle, and performing iterative calculation, wherein the maximum value of the torque in the iterative process is used as the limit torque after the shearing force is considered.
Further, in the step S2, the calculation formula of the total area of the vertical plate grid cells is:
Wherein n is the total number of plate panels, l i is the width of the ith plate panel, and mm; t i is the thickness of the ith plate panel, mm; sin theta i is the included angle between the ith plate grid and the horizontal line;
the shear stress of the vertical plate grid is as follows:
F is the applied shearing force, and in addition, shearing stress exists in the horizontal plate grid of the thin-wall beam due to the circulation effect of shearing flow; and according to the shear flow distribution rule under the action of the thin wall Liang Chunjian, the shear stress of the horizontal plate is calculated by combining the shear stress of the vertical plate.
Still further, in the step S3, for the plate limit shear stress τ C of the four-side simple support, the calculation formula is as follows:
Wherein τ C is the ultimate shear strength of the plate lattice; r eH-P is the material yield strength of the panel, N/mm 2;Cτ is the buckling reduction factor, and there are:
lambda is the reference slenderness ratio of the plate lattice, and is:
K is the buckling factor, and is:
σ E is the reference stress of the plate grid, N/mm 2;
wherein E is the elastic modulus of the material, and N/mm 2; t is the thickness of the plate lattice net, and mm; a. b is the length and width of the plate lattice, mm;
according to the obtained shear stress under the shearing force and the limit shear stress of the plate, the torsion limit shear stress after the shearing force is calculated, and the calculation formula is as follows:
τcr＝τC-τs
Wherein τ cr is the torsional limit shear stress after the shear force is considered, N/mm 2;τC is the plate limit shear stress, N/mm 2;τs is the plate shear stress under the shear force, and N/mm 2.
In the 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 lattice, mm 2, t is the net thickness of the plate lattice, mm 2, E is the elastic modulus of the material, N/mm 2,ReH-p is the yield strength of the material of the plate lattice, and N/mm 2;
according to the attribute of the plate width-thickness ratio, a curve relationship between shear stress and shear strain in the plate grid torsion process is constructed as follows:
Wherein, gamma E is the unit strain, gamma y is the strain at which the unit reaches yield, determined by the following formula:
Where R eH-P is the material yield strength of the panel, N/mm 2, and G is the shear modulus.
In the step S5, an initial torsion angle is given to the thin-wall beam, the strain of each plate at the initial torsion angle is calculated according to the distance from the plate to the centroid of the cross section, the shear stress of each plate is calculated according to the relation between the shear stress and the shear strain, the shear force of each plate is obtained by multiplying the area of the plate, the moment is obtained by multiplying the distance from the plate to the centroid of the cross section, and the moment of all the plates is accumulated to obtain the torque of the thin-wall beam section constraint torsion at the initial torsion angle.
The beneficial effects of the invention are mainly shown in the following steps: the method is applied to calculating the ultimate bearing capacity of the thin-wall beam under the shearing and twisting combined load action. And checking and calculating the two container real ships, analyzing and comparing the formula calculation value and the finite element calculation value, and finding that the formula calculation value has smaller phase difference with the finite element simulation result and has higher precision.
The method can calculate the limit bearing capacity of the constraint torsion of the thin-wall beam rapidly and accurately.
Drawings
FIG. 1 is a flow chart of a method for calculating the ultimate strength of a thin-walled beam under the action of a shear-torsion combined load.
FIG. 2 is a schematic diagram of a thin-walled beam section in cell division under shear and torsion.
FIG. 3 is a graph of the shear flow profile under the influence of a thin wall Liang Chunjian, wherein (a) the shear flow profile at the sidewall is hypothesized; (b) a double-layer bottom shear flow distribution hypothesis graph.
Fig. 4 is a flow chart of the ultimate strength calculation of a thin-walled beam under a 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-wall beam under the action of shear-torsion combined load comprises the following steps:
S1, dispersing a thin-wall beam section into lattice units according to positions of strengthening materials and longitudinal bones in the section, establishing a thin-wall beam section single-span calculation model, and inputting basic material properties, wherein the basic material properties comprise yield strength, elastic modulus and Poisson' S ratio of the section material;
S2, applying shearing force, adding up the sum of the cross-sectional areas of the vertical members of the thin-wall beam section, neglecting the shearing resistance and torsion resistance of the aggregate members, calculating the shearing stress of the vertical plate panels, and calculating the shearing stress of each horizontal plate panel in the section according to the shearing flow distribution assumption of the limit state under the pure shearing action;
S3, calculating the limit shear stress of the plate, bringing the shear stress of the plate into a limit state stress equation of the plate, and calculating to obtain the torsional limit shear stress taking the shear effect into consideration;
S4, calculating the width-to-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 S5, applying a torsion angle to the thin-wall beam, calculating the shear strain of each plate grid, calculating the shear stress of each plate grid according to the shear stress-strain relation, calculating the contribution of each plate grid to the torque to obtain the torque, increasing the torsion angle, and performing iterative calculation, wherein the maximum value of the torque in the iterative process is used as the limit torque after the shearing force is considered.
In the step S2, shearing force is applied, the sum of the cross-sectional areas of the vertical members with the thin-wall beam cross-section is summed, the shearing resistance and the torsion resistance of the members such as bone materials are ignored, the shearing stress of the vertical plate panels is calculated, and the shearing stress of each horizontal plate panel in the cross-section is calculated according to the assumption of shearing 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 plate panels, l i is the width of the ith plate panel, and mm; t i is the thickness of the ith plate panel, mm; sin theta i is the included angle between the ith plate grid and the horizontal line.
The shear stress of the vertical plate grid is as follows:
f is the applied shearing force, and in addition, due to the circulation effect of shearing flow, certain shearing stress exists in the horizontal plate grid of the thin-wall beam, and the distribution rule of the shearing stress is shown in figure 2.
And according to the shear flow distribution rule under the action of the thin wall Liang Chunjian, the shear stress of the horizontal plate is calculated by combining the shear stress of the vertical plate.
In the step S3, the ultimate shear stress of the plate is calculated, the ultimate shear stress of the plate is brought into the ultimate state stress equation of the plate, and the ultimate shear stress of the torsion is calculated and obtained after the shearing force is considered.
For the limit shearing stress tau C of the plate grid with the simple four sides, the specific calculation formula is as follows:
Wherein τ C is the ultimate shear strength of the plate lattice; r eH-p is the material yield strength of the panel, N/mm 2;Cτ is the buckling reduction factor, and there are:
lambda is the reference slenderness ratio of the plate lattice, and is:
K is the buckling factor, and is:
σ E is the reference stress of the plate grid, N/mm 2;
wherein E is the elastic modulus of the material, and N/mm 2; t is the thickness of the plate lattice net, and mm; a. b is the length and width of the panel, mm, respectively.
According to the obtained shear stress under the shearing force and the limit shear stress of the plate, the torsion limit shear stress after the shearing force is calculated, and the calculation formula is as follows:
τcr＝τC-τs
Wherein τ cr is the torsional limit shear stress after the shear force is considered, N/mm 2;τC is the plate limit shear stress, N/mm 2;τs is the plate shear stress under the shear force, and N/mm 2.
In the step S4, calculating the width-to-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;
beta is the width-thickness ratio of the plate, and the calculation formula is as follows:
Wherein b is the width of the plate lattice, mm 2, t is the net thickness of the plate lattice, mm 2, E is the elastic modulus of the material, N/mm 2,ReH-p is the yield strength of the material of the plate lattice, and N/mm 2;
according to the attribute of the plate width-thickness ratio, a curve relationship between shear stress and shear strain in the plate grid torsion process is constructed as follows:
Where γ E is the unit strain and γ y is the strain at which the unit reaches yield, as determined by:
Where R eH-P is the material yield strength of the panel, N/mm 2, and G is the shear modulus.
In the step S5, an initial torsion angle is given to the thin-wall beam, the strain of each plate at the initial torsion angle is calculated according to the distance from the plate to the centroid of the cross section, the shear stress of each plate is calculated according to the relation between the shear stress and the shear strain, the shear force of each plate is obtained by multiplying the area of the plate, the moment is obtained by multiplying the distance from the plate to the centroid of the cross section, and the moment of all the plates is accumulated to obtain the torque of the thin-wall beam section constraint torsion at the initial torsion angle.
Knowing the shearing force of the plate grid at the initial torsion angle, calculating the moment of the plate grid to the cross section core, and accumulating the moment of all the plate grids to obtain the torque of the thin-wall beam section constraint torsion at the initial torsion angle. A specific computational flow diagram is shown in fig. 4.
To verify the accuracy of the proposed method, two container ships and ocean platforms were checked and compared with finite elements, and table 1 is a combined ultimate strength comparison (shear 10 8 N, torque 10 13 n·mm) for container ship shear No. 1.
TABLE 1
Table 2 shows the ultimate strength of the shear-torsion combination of container ship No. 2 (shear 10 8 N, torque 10 13 N.mm).
TABLE 2
The embodiments described in this specification are merely illustrative of the manner in which the inventive concepts may be implemented. The scope of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, but the scope of the present invention and the equivalents thereof as would occur to one skilled in the art based on the inventive concept.

Claims (1)

1. The method for calculating the ultimate strength of the thin-wall beam under the action of shear-torsion combined load is characterized by comprising the following steps of:
S1, dispersing a thin-wall beam section into lattice units according to positions of strengthening materials and longitudinal bones in the section, establishing a thin-wall beam section single-span calculation model, and inputting basic material properties, wherein the basic material properties comprise yield strength, elastic modulus and Poisson' S ratio of the section material;
S2, applying shearing force, adding up the sum of the cross-sectional areas of the vertical members of the thin-wall beam section, neglecting the shearing resistance and torsion resistance of the aggregate members, calculating the shearing stress of the vertical plate panels, and calculating the shearing stress of each horizontal plate panel in the section according to the shearing flow distribution assumption of the limit state under the pure shearing action;
S3, calculating the limit shear stress of the plate, bringing the shear stress of the plate into a limit state stress equation of the plate, and calculating to obtain the torsional limit shear stress taking the shear effect into consideration;
S4, calculating the width-to-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;
S5, applying a torsion angle to the thin-wall beam, calculating the shear strain of each plate grid, calculating the shear stress of each plate grid according to the shear stress-strain relation, calculating the contribution of each plate grid to the torque to obtain the torque, increasing the torsion angle for iterative calculation, and taking the maximum value of the torque in the iterative process as the limit torque after the shear force is considered;
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 plate panels, l i is the width of the ith plate panel, and mm; t i is the thickness of the ith plate panel, mm; sin theta i is the included angle between the ith plate grid and the horizontal line;
the shear stress of the vertical plate grid is as follows:
f is the applied shearing force, and in addition, shearing stress exists in the horizontal plate grid of the thin-wall beam due to the circulation effect of shearing flow; according to the shear flow distribution rule under the action of the thin wall Liang Chunjian, the shear stress of the horizontal plate is calculated by combining the shear stress of the vertical plate;
In the step S3, for the limit shear stress τ C of the plate lattice with the simple four sides, the calculation formula is as follows:
Wherein τ C is the ultimate shear strength of the plate lattice; r eH-P is the material yield strength of the panel, N/mm 2;Cτ is the buckling reduction factor, and there are:
lambda is the reference slenderness ratio of the plate lattice, and is:
K is the buckling factor, and is:
σ E is the reference stress of the plate grid, N/mm 2;
wherein E is the elastic modulus of the material, and N/mm 2; t is the thickness of the plate lattice net, and mm; a. b is the length and width of the plate lattice, mm;
according to the obtained shear stress under the shearing force and the limit shear stress of the plate, the torsion limit shear stress after the shearing force is calculated, and the calculation formula is as follows:
τcr＝τC-τs
Wherein τ cr is the torsional limit shear stress after the shearing action is considered, N/mm 2;τC is the plate limit shear stress, N/mm 2;τs is the plate shear stress under the shearing action, and N/mm 2;
In the 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 lattice, mm 2, t is the net thickness of the plate lattice, mm 2, E is the elastic modulus of the material, N/mm 2,ReH-P is the yield strength of the material of the plate lattice, and N/mm 2;
according to the attribute of the plate width-thickness ratio, a curve relationship between shear stress and shear strain in the plate grid torsion process is constructed as follows:
Wherein, gamma E is the unit strain, gamma y is the strain at which the unit reaches yield, determined by the following formula:
Wherein R eH-P is the material yield strength of the plate lattice, N/mm 2, G is the shear modulus;
In the step S5, an initial torsion angle is given to the thin-wall beam, the strain of each plate at the initial torsion angle is calculated according to the distance from the plate to the centroid of the cross section, the shear stress of each plate is calculated according to the relation between the shear stress and the shear strain, the shear force of each plate is obtained by multiplying the area of the plate, the moment is obtained by multiplying the distance from the plate to the centroid of the cross section, and the moment of all the plates is accumulated to obtain the torque of the thin-wall beam section constraint torsion at the initial torsion angle.
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Citations (2)

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CN108562421A (en) * 2018-04-18 2018-09-21 中国船舶工业集团公司第七0八研究所 A kind of small waterplane area twin hull ship bending joint ultimate strength test design methods
CN110119592A (en) * 2019-05-22 2019-08-13 中国船舶工业集团公司第七0八研究所 A kind of calculation method of hull beam constraint torsion ultimate bearing capacity

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KR20110113344A (en) * 2010-04-09 2011-10-17 삼성중공업 주식회사 Evaluation system for post-buckling strength and behaviour of the curved plate and method thereof
CN110362940B (en) * 2019-07-19 2022-05-17 中国船舶科学研究中心（中国船舶重工集团公司第七0二研究所） Method for calculating ultimate bearing capacity of ocean engineering structure under complex load effect

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108562421A (en) * 2018-04-18 2018-09-21 中国船舶工业集团公司第七0八研究所 A kind of small waterplane area twin hull ship bending joint ultimate strength test design methods
CN110119592A (en) * 2019-05-22 2019-08-13 中国船舶工业集团公司第七0八研究所 A kind of calculation method of hull beam constraint torsion ultimate bearing capacity

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