A method for designing the structural parameters of an i-beam cross section

Abstract

The application belongs to the technical field of I-beam cross-section structure parameter design, and particularly relates to an I-beam cross-section structure parameter design method, which comprises the following steps: determining structure design parameters of an I-beam cross-section; calculating a cross-section area of the I-beam based on the structure design parameters; calculating a critical load of compression instability of the I-beam based on the structure design parameters; designing constraints among the structure design parameters and designing a cross-section area constraint, and finding structure design parameters that maximize the critical load of compression instability of the I-beam.

Description

A method for designing the cross-sectional structural parameters of an I-beam Technical Field

[0001] This application belongs to the technical field of I-beam cross-section structural parameter design, specifically relating to a method for designing I-beam cross-section structural parameters. Background Technology

[0002] I-beams have advantages such as high bending resistance, light weight, easy processing, and low cost, and are widely used in engineering. Currently, the cross-sectional structural parameters of I-beams have been standardized. However, these standardized cross-sectional structural parameters are not optimal under certain specific environments. By designing the cross-sectional structural parameters, I-beams can have better resistance to compressive instability and relatively small mass, which is of great significance to the aerospace field. Therefore, this application is proposed.

[0003] It should be noted that the above background information is only used to assist in understanding the inventive concept and technical solution of this invention, and it does not necessarily belong to the prior art of this patent application. In the absence of clear evidence that the above information was disclosed on the filing date of this application, the above background information should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0004] The purpose of this application is to provide a method for designing the structural parameters of an I-beam cross-section, so as to overcome or mitigate at least one of the known technical defects.

[0005] The technical solution of this application is:

[0006] A method for designing the cross-sectional structural parameters of an I-beam includes:

[0007] Determine the structural design parameters of the I-beam cross-section;

[0008] Calculate the cross-sectional area of ​​the I-beam based on the structural design parameters;

[0009] Calculate the critical load for compressive instability of the I-beam based on structural design parameters;

[0010] By considering the constraints between structural design parameters and the constraints on the cross-sectional area, we can find the structural design parameters that maximize the critical load for compressive instability of the I-beam.

[0011] According to at least one embodiment of this application, in the above-described design method for the structural parameters of the I-beam cross section, the structural design parameters of the I-beam cross section include the distance h1 between the inner sides of the two side flanges, the distance h2 between the outer sides of the two side flanges, the distance h3 between the tops of the convex edges on the two side flanges, the width w1 of the web, the distance w2 between the inner sides of the two convex edges on the flange, and the distance w3 between the outer sides of the two convex edges on the flange.

[0012] According to at least one embodiment of this application, in the above-described method for designing the cross-sectional structural parameters of an I-beam, the calculation of the cross-sectional area of ​​the I-beam based on the structural design parameters specifically involves:

[0013]

[0014] in,

[0015] S is the cross-sectional area of ​​the I-beam.

[0016] According to at least one embodiment of this application, in the above-described method for designing the structural parameters of an I-beam cross-section, the critical load for compressive instability of the I-beam is calculated based on the structural design parameters, specifically as follows:

[0017]

[0018]

[0019] P cr =σ 0.2 S, λ < 20;

[0020]

[0021]

[0022]

[0023] I min =min(I x ,I y );

[0024] ;

[0025]

[0026] in,

[0027] P cr This is the critical load for the compressive instability of the I-beam;

[0028] E is the elastic modulus of the I-beam material;

[0029] λ is the effective slenderness ratio of the I-beam;

[0030] E t Tangent modulus of the I-beam material;

[0031] σ 0.2The tensile yield strength of the I-beam material;

[0032] ρ is the radius of gyration of the I-beam cross section;

[0033] L′ is the effective length of the I-beam;

[0034] L is the length of the I-beam;

[0035] C is the support coefficient of the I-beam;

[0036] I min This is the smaller of the moments of inertia of the I-beam section in the x and y directions;

[0037] I x Let be the moment of inertia of the I-beam section in the x-direction;

[0038] I y Let be the moment of inertia of the I-beam section in the y-direction.

[0039] According to at least one embodiment of this application, in the above-described design method for the structural parameters of the I-beam cross-section, when the I-beam is subjected to axial load at the end and is hinged at both ends, C = 1;

[0040] When the I-beam is subjected to axial load at its ends and is fixed at both ends, C = 4;

[0041] When an I-beam is subjected to axial load at its end, with the upper end hinged and the lower end fixed,

[0042] C = 2.05;

[0043] When an I-beam is subjected to an axial load at its end, with the upper end free and the lower end fixed,

[0044] C = 0.25;

[0045] When the I-beam is subjected to a uniform axial load and is hinged at both ends, C = 1.87;

[0046] When the I-beam is subjected to a uniform axial load and is fixed at both ends, C = 7.5;

[0047] When an I-beam is subjected to a uniform axial load, with the upper end hinged and the lower end fixed,

[0048] C = 6.08;

[0049] When an I-beam is subjected to a uniform axial load, with the upper end free and the lower end fixed,

[0050] C = 0.794.

[0051] According to at least one embodiment of this application, in the above-described method for designing the structural parameters of an I-beam cross-section, the constraints between the structural design parameters are specifically as follows:

[0052] h3-h2>a, a≥0;

[0053] h2-h1>b, b≥0;

[0054] w1>c, c≥0;

[0055] w3-w2>d, d≥0;

[0056] h1>e, e≥0;

[0057] w2-w1>f, f≥0.

[0058] According to at least one embodiment of this application, in the above-described design method for I-beam cross-sectional structural parameters, the design cross-sectional area constraint is specifically as follows:

[0059] S-nS int ≤0;

[0060] 0 <n≤1;

[0061]

[0062] in,

[0063] S int This represents the initial area of ​​the I-beam cross-section;

[0064] h 10 h 20 h 30 w 10 w 20 w 30 The initial values ​​are: h1 between the inner sides of the two side flanges of the I-beam section, h2 between the outer sides of the two side flanges, h3 between the tops of the convex edges on the two side flanges, w1 for the width of the web, w2 between the inner sides of the two convex edges on the flange, and w3 between the outer sides of the two convex edges on the flange. Attached Figure Description

[0065] Figure 1 is a schematic diagram of the design method for I-beam cross-section structural parameters provided in an embodiment of this application;

[0066] Figure 2 is a schematic diagram of the cross-section of the I-beam provided in an embodiment of this application.

[0067] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual size of the product. Furthermore, the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Detailed Implementation

[0068] To make the technical solution and advantages of this application clearer, the technical solution of this application will be described in a clearer and more complete manner below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only some embodiments of this application, and are only used to explain this application, not to limit this application. It should be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings. Other related parts can be referred to the general design. In the absence of conflict, the embodiments and technical features in the embodiments of this application can be combined with each other to obtain new embodiments.

[0069] Furthermore, unless otherwise defined, the technical or scientific terms used in this application description shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms "upper," "lower," "left," "right," "center," "vertical," "horizontal," "inner," and "outer," etc., used in this application description to indicate relative direction or positional relationship are used only to indicate relative orientation or positional relationship, and do not imply that the device or component must have a specific orientation, or be constructed and operated in a specific orientation. When the absolute position of the described object changes, its relative positional relationship may also change accordingly, and therefore should not be construed as a limitation on this application. The terms "first," "second," "third," and similar terms used in this application description are used only for descriptive purposes to distinguish different components, and should not be construed as indicating or implying relative importance. The terms "a," "one," or "the," etc., used in this application description should not be construed as an absolute limitation on quantity, but should be construed as indicating the existence of at least one. The terms "including," "comprising," etc., used in this application description mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, without excluding other elements or objects.

[0070] Furthermore, it should be noted that, unless otherwise explicitly specified and limited, terms such as “installation,” “connection,” and “linkage” used in the description of this application should be interpreted broadly. For example, a connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; or it can be a connection within two components. Those skilled in the art can understand its specific meaning in this application according to the specific circumstances.

[0071] The present application will now be described in further detail with reference to Figures 1 and 2.

[0072] A method for designing the cross-sectional structural parameters of an I-beam includes:

[0073] Determine the structural design parameters of the I-beam cross-section;

[0074] Calculate the cross-sectional area of ​​the I-beam based on the structural design parameters;

[0075] Calculate the critical load for compressive instability of the I-beam based on structural design parameters;

[0076] By considering the constraints between structural design parameters and the constraints on the cross-sectional area, we can find the structural design parameters that maximize the critical load for compressive instability of the I-beam.

[0077] Regarding the design method for the structural parameters of the I-beam section disclosed in the above embodiments, those skilled in the art can understand that, under the constraints of structural design parameters and cross-sectional area, the design seeks the structural design parameters that maximize the critical load for compressive instability of the I-beam, thereby completing the design of the structural parameters of the I-beam section. This can result in the I-beam having better resistance to instability and relatively smaller mass.

[0078] In some optional embodiments, the structural design parameters of the I-beam cross-section in the above-mentioned design method include the following structural design parameters: the distance between the inner sides of the two side flanges of the I-beam cross-section is h1, the distance between the outer sides of the two side flanges is h2, the distance between the tops of the convex edges on the two side flanges is h3, the width of the web is w1, the distance between the inner sides of the two convex edges on the flange is w2, and the distance between the outer sides of the two convex edges on the flange is w3.

[0079] In some optional embodiments, the above-described method for designing the cross-sectional structural parameters of an I-beam involves calculating the cross-sectional area of ​​the I-beam based on the structural design parameters, specifically as follows:

[0080]

[0081] in,

[0082] S is the cross-sectional area of ​​the I-beam.

[0083] In some optional embodiments, the above-described design method for I-beam cross-section structural parameters involves calculating the critical load for compressive instability of the I-beam based on the structural design parameters, specifically as follows:

[0084]

[0085]

[0086] P cr =σ 0.2 S, λ < 20;

[0087]

[0088]

[0089]

[0090] I min =min(I x ,I y );

[0091] ;

[0092]

[0093] in,

[0094] P cr This is the critical load for the compressive instability of the I-beam;

[0095] E is the elastic modulus of the I-beam material;

[0096] λ is the effective slenderness ratio of the I-beam;

[0097] E t Tangent modulus of the I-beam material;

[0098] σ 0.2 The tensile yield strength of the I-beam material;

[0099] ρ is the radius of gyration of the I-beam cross section;

[0100] L ′ This is the effective length of the I-beam;

[0101] L is the length of the I-beam;

[0102] C is the support coefficient of the I-beam;

[0103] I min This is the smaller of the moments of inertia of the I-beam section in the x and y directions;

[0104] I x Let be the moment of inertia of the I-beam section in the x-direction;

[0105] I y Let be the moment of inertia of the I-beam section in the y-direction.

[0106] In some optional embodiments, in the above-described design method for the structural parameters of the I-beam cross-section, when the I-beam is subjected to axial load at the end and is hinged at both ends, C = 1;

[0107] When the I-beam is subjected to axial load at its ends and is fixed at both ends, C = 4;

[0108] When the I-beam is subjected to axial load at the end, with the upper end hinged and the lower end fixed, C = 2.05;

[0109] When the I-beam is subjected to axial load at the end, with the upper end free and the lower end fixed, C = 0.25;

[0110] When the I-beam is subjected to a uniform axial load and is hinged at both ends, C = 1.87;

[0111] When the I-beam is subjected to a uniform axial load and is fixed at both ends, C = 7.5;

[0112] When the I-beam is subjected to a uniform axial load, with the upper end hinged and the lower end fixed, C = 6.08;

[0113] When the I-beam is subjected to a uniform axial load, with the upper end free and the lower end fixed, C = 0.794.

[0114] In some optional embodiments, the design method for the structural parameters of the I-beam section described above includes the following specific steps for designing constraints between structural design parameters:

[0115] h3-h2>a, a≥0;

[0116] h2-h1>b, b≥0;

[0117] w1>c, c≥0;

[0118] w3-w2>d, d≥0;

[0119] h F >e, e≥0;

[0120] w2-w 17 >f, f≥0;

[0121] in,

[0122] a, b, c, d, e, and f can be chosen from values ​​within the required range based on actual needs.

[0123] In some optional embodiments, the design method for the structural parameters of the I-beam cross-section described above includes designing cross-sectional area constraints, specifically as follows:

[0124] S-nS int ≤0;

[0125] 0 <n≤1;

[0126]

[0127] in,

[0128] S intThis represents the initial area of ​​the I-beam cross-section;

[0129] h 10 h 20 h 30 w 10 w 20 w 30 The initial values ​​are: h1 between the inner sides of the two side flanges of the I-beam section, h2 between the outer sides of the two side flanges, h3 between the tops of the convex edges on the two side flanges, w1 for the width of the web, w2 between the inner sides of the two convex edges on the flange, and w3 between the outer sides of the two convex edges on the flange.

[0130] In one specific embodiment, the I-beam is made of TC18 steel, subjected to axial loads at both ends, and hinged at both ends, with L = 1000 mm and h... 10 =12mm, h 20 =28mm, h 30 =50mm, w 10 =4mm, w 20 =15mm, w 30 =45mm. The structural parameters were optimized using the I-beam cross-section structural parameter design method disclosed in the above embodiment. The parameters were set as n=0.8, a=0, b=12, c=6, d=0, e=0, f=0. The fmincon function in the optimization toolbox of Matlab was used to solve the problem. The results are compared below:

[0131]

[0132] As can be seen from the above, by adopting the optimized structural design parameters, the critical load for compressive instability of the I-beam increased from the initial 309420 to 371660, improving the compressive instability resistance by 20.12%. At the same time, the cross-sectional area decreased from the initial 1428 to 1138, and the weight was reduced by 20.3% while keeping the length of the I-beam unchanged.

[0133] The various embodiments in the specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0134] The technical solution of this application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of this application is obviously not limited to these specific embodiments. Without departing from the principles of this application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of this application.

Claims

1. A method for designing the structural parameters of an I-beam cross-section, characterized in that, include: Determine the structural design parameters of the I-beam cross-section; Calculate the cross-sectional area of ​​the I-beam based on the structural design parameters; Calculate the critical load for compressive instability of the I-beam based on structural design parameters; The design involves constraining structural design parameters and cross-sectional area to find the structural design parameters that maximize the critical load for compressive instability of the I-beam. The structural design parameters for the I-beam cross-section include the distance between the inner sides of the two side flanges of the I-beam cross-section. Distance between the outer sides of the two side plates Distance between the top edges of the protruding edges on both side plates Width of the web Distance between the inner sides of the two convex edges on the flange plate Distance between the outer sides of the two convex edges on the flange plate The critical load for compressive instability of the I-beam is calculated based on the structural design parameters, specifically as follows: ， ； ， ； ， ； ； ； ； ； ； ;in, This is the critical load for the compressive instability of the I-beam; The elastic modulus of the I-beam material; The effective slenderness ratio of the I-beam; Tangent modulus of the I-beam material; The tensile yield strength of the I-beam material; The radius of gyration of the I-beam cross section; This is the effective length of the I-beam; This refers to the length of the I-beam; The support coefficient of the I-beam; This is the smaller of the moments of inertia of the I-beam section in the x and y directions; Let be the moment of inertia of the I-beam section in the x-direction; Let be the moment of inertia of the I-beam section in the y-direction; This represents the cross-sectional area of ​​the I-beam.

2. The design method for I-beam cross-section structural parameters according to claim 1, characterized in that, The cross-sectional area of ​​the I-beam is calculated based on the structural design parameters, specifically as follows: 。 3. The method for designing the structural parameters of an I-beam section according to claim 2, characterized in that, When an I-beam is subjected to axial load at its ends and is hinged at both ends, When an I-beam is subjected to axial load at its ends and is fixed at both ends, When an I-beam is subjected to axial load at its end, with the upper end hinged and the lower end fixed, When an I-beam is subjected to an axial load at its end, with the upper end free and the lower end fixed, When an I-beam is subjected to a uniform axial load and is hinged at both ends, When an I-beam is subjected to a uniform axial load and is fixed at both ends, When an I-beam is subjected to a uniform axial load, with the upper end hinged and the lower end fixed, When an I-beam is subjected to a uniform axial load, with the upper end free and the lower end fixed, 。 4. The method for designing the structural parameters of an I-beam section according to claim 3, characterized in that, The constraints between structural design parameters are as follows: ， ； ， ； ， ； ， ； ， ； ， 。 5. The method for designing the structural parameters of an I-beam section according to claim 4, characterized in that, Design cross-sectional area constraints, specifically: ； ； ;in, This represents the initial area of ​​the I-beam cross-section; The distance between the inner sides of the two edge plates of the I-beam section Distance between the outer sides of the two side plates Distance between the top edges of the protruding edges on both side plates Width of the web Distance between the inner sides of the two convex edges on the flange plate Distance between the outer sides of the two convex edges on the flange plate The initial value.

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