CN117951804A - I-shaped longitudinal beam design method for bearing uniformly distributed load - Google Patents
I-shaped longitudinal beam design method for bearing uniformly distributed load Download PDFInfo
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Abstract
The application belongs to the field of aviation structural strength design, and particularly relates to an I-shaped longitudinal beam design method for bearing uniformly distributed loads. Comprising the following steps: calculating uniform load born by the longitudinal beam; calculating the shearing force and bending moment of the profile of the longitudinal beam according to the uniformly distributed load born by the longitudinal beam; calculating the neutral layer position of the longitudinal beam; calculating bending moment of inertia of the longitudinal beam section; calculating the maximum axial tensile stress of the edge strips of the longitudinal beams subjected to stretching and the axial compressive stress of the edge strips of the longitudinal beams subjected to compression; calculating the areas of the upper and lower edge strips of the longitudinal beam according to the maximum axial tensile stress and the axial compressive stress of the edge strips; and calculating the thickness of the girder web according to the shearing force of the girder section. The application starts from the analysis of the uniform load transmission of the fuselage typical structure, and clearly shows the relation between the rigidity calculation method and the section stress calculation method of the uniform load beam, and forms the stress control design method of the uniform load beam, thereby obtaining the calculation mode of each parameter of the I-shaped longitudinal beam.
Description
Technical Field
The application belongs to the field of aviation structural strength design, and particularly relates to an I-shaped longitudinal beam design method for bearing uniformly distributed loads.
Background
The structures such as the airtight floor of the cockpit of the transportation aircraft body, the airtight top plate of the wing body butt joint area, the airtight floor of the main connecting area, the airtight bulkhead of the cockpit, the airtight end frame of the freight cabin and the like are generally subjected to severe airtight loads, the structures are generally composed of reinforcing longitudinal beams, reinforcing ribs and thin plates, the airtight loads are finally transferred to the reinforcing longitudinal beams through skins and reinforcing ribs, and the longitudinal beams are mainly subjected to shearing and bending caused by uniformly distributed loads. The longitudinal beam is used as an important component for transmitting airtight load of the structure, and the rigidity and strength design of the longitudinal beam is not provided with a clear design instruction document, so that the domestic aircraft design often has the design problems of unreasonable rigidity arrangement, large stress gradient and the like, and the economical efficiency, the safety and the service life of the aircraft are affected. The height design of the I-shaped longitudinal beam, the rigidity matching design along the length direction, the cross section size design of the upper and lower edge strips, the thickness design of the web plate, the equal stress design of the edge strips, the maximum stress control design of the cross section are related to the service life, the structural weight, the use economy and the like of the airplane. The design efficiency cannot be improved without explicit guide files when the longitudinal beam is reinforced, the manpower resource waste is caused, the weight is not optimal, the economy of the aircraft is poor, the maximum stress of the design cannot be accurately controlled, and the service life and the flight safety of the aircraft are affected.
The design of the longitudinal beam structure at home and abroad mainly depends on the common design manual reference to design the section of the longitudinal beam structure, but no systematic design method exists, the design experience of a designer for many years is needed, or the layout optimization is carried out by adopting a finite element method, but the process is relatively complex, and the method is not applicable to the design stage of a scheme.
It is therefore desirable to have a solution that overcomes or at least alleviates at least one of the above-mentioned drawbacks of the prior art.
Disclosure of Invention
The application aims to provide an I-shaped longitudinal beam design method for bearing uniformly distributed loads, which aims to solve at least one problem in the prior art.
The technical scheme of the application is as follows:
the design method of the I-shaped longitudinal beam for bearing uniformly distributed loads is characterized by comprising the following steps of:
Step one, calculating uniform load born by a longitudinal beam;
step two, calculating the shearing force and bending moment of the profile of the longitudinal beam according to the uniformly distributed load born by the longitudinal beam;
step three, calculating the neutral layer position of the longitudinal beam;
step four, calculating bending moment of inertia of the longitudinal beam section;
calculating the maximum axial tensile stress of the edge strips of the longitudinal beams subjected to stretching and the axial compressive stress of the edge strips of the longitudinal beams subjected to compression;
step six, calculating the areas of the upper and lower edge strips of the longitudinal beam according to the maximum axial tensile stress and the axial compressive stress of the edge strips;
And step seven, calculating the thickness of the girder web plate according to the shearing force of the girder section.
In at least one embodiment of the present application, in step one, the calculating the uniform load born by the stringers includes:
the uniformly distributed load born by the longitudinal beam is as follows:
q＝p*Δl
Wherein q is the uniform load born by the longitudinal beam, p is the uniform surface load born by the wall plates at two sides of the longitudinal beam, and Deltal is the width of the wall plates at two sides of the longitudinal beam.
In at least one embodiment of the present application, in the second step, the calculating the shear force and the bending moment of the profile of the stringer according to the uniformly distributed load born by the stringer includes:
the shear force of the profile of the longitudinal beam is calculated according to the uniformly distributed load born by the longitudinal beam, and is as follows:
the bending moment of the profile of the longitudinal beam is calculated according to the uniformly distributed load born by the longitudinal beam, and is as follows:
wherein Q x is the shear force of the profile of the longitudinal beam, M x is the bending moment of the profile of the longitudinal beam, and x is the distance from any point to the starting point by taking one end of the longitudinal beam as the starting point.
In at least one embodiment of the present application, in step three, the calculating the neutral layer position of the stringer includes:
the neutral layer position of the longitudinal beam is:
Wherein H is the neutral layer position of the longitudinal beam, a is the area of the upper edge strip of the longitudinal beam, b is the area of the lower edge strip of the longitudinal beam, and H is the height of the longitudinal beam.
In at least one embodiment of the present application, in step four, the calculating a bending moment of inertia of the stringer profile includes:
the bending moment of inertia of the longitudinal beam profile is:
I＝a(H-h)2+bh2
wherein I is the bending moment of inertia of the cross section of the longitudinal beam.
In at least one embodiment of the present application, in step five, the calculating the maximum axial tensile stress of the edge strip subjected to stretching and the axial compressive stress of the edge strip subjected to compression includes:
The maximum axial tensile stress of the edge strip of the longitudinal beam which bears the tension is as follows:
The axial compressive stress of the edge strip of the longitudinal beam bearing compression is as follows:
Wherein σ t is the maximum axial tensile stress of the cap and σ c is the axial compressive stress of the cap.
In at least one embodiment of the present application, in step six, the maximum axial tensile stress formula and the axial compressive stress formula of the cap are solved in combination, so as to obtain the area of the cap on the longitudinal beam as follows:
the area of the longitudinal beam lower edge strip is as follows:
in at least one embodiment of the present application, in step seven, the calculating the thickness of the stringer web according to the shearing force of the stringer profile includes:
the thickness of the stringer web is determined according to the following formula:
Wherein τ cr is shear instability stress of a longitudinal beam web, K s is boundary support coefficient of the longitudinal beam web, E is elastic modulus of the material, mu is Poisson's ratio of the material, and t is thickness of the longitudinal beam web.
The invention has at least the following beneficial technical effects:
According to the design method of the I-shaped longitudinal beam for bearing the uniform load, provided by the application, from the analysis of the transmission load of the uniform load borne by the fuselage typical structure, the relation between the rigidity calculation method and the section stress calculation method of the uniform load beam is clarified, the stress control design method of the uniform load beam is formed, the calculation mode of each parameter of the I-shaped longitudinal beam is obtained, and the strength design of the uniform load beam can be guided.
Drawings
FIG. 1 is a schematic illustration of an I-beam of one embodiment of the present application;
FIG. 2 is a schematic illustration of a two-end simply supported uniform load beam in accordance with one embodiment of the present application;
FIG. 3 is a schematic view of a fuselage subjected to uniform load in accordance with one embodiment of the present application;
FIG. 4 is a stringer cross-section shear profile of one embodiment of the present application;
FIG. 5 is a profile of a stringer cross-section bending moment profile of one embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application become more apparent, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of the application. The embodiments described below by referring to the drawings are illustrative and intended to explain the present application and should not be construed as limiting the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application. Embodiments of the present application will be described in detail below with reference to the accompanying drawings.
In the description of the present application, it should be understood that the terms "center," "longitudinal," "lateral," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, merely to facilitate describing the present application and simplify the description, and do not indicate or imply that the devices or elements being referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the scope of the present application.
The application is described in further detail below with reference to fig. 1 to 5.
The application provides a design method of an I-shaped longitudinal beam for bearing uniform load, in particular to a rigidity strength design method when an I-shaped longitudinal beam structure with simple supports at two ends in the detailed design stage of an airplane bears uniform load, wherein the I-shaped longitudinal beam is shown in figure 1, and uniform load beams with simple supports at two ends are shown in figure 2.
The application relates to an I-shaped longitudinal beam design method for bearing uniformly distributed loads, which comprises the following steps:
Step one, calculating uniform load born by a longitudinal beam;
step two, calculating the shearing force and bending moment of the profile of the longitudinal beam according to the uniformly distributed load born by the longitudinal beam;
step three, calculating the neutral layer position of the longitudinal beam;
step four, calculating bending moment of inertia of the longitudinal beam section;
calculating the maximum axial tensile stress of the edge strips of the longitudinal beams subjected to stretching and the axial compressive stress of the edge strips of the longitudinal beams subjected to compression;
step six, calculating the areas of the upper and lower edge strips of the longitudinal beam according to the maximum axial tensile stress and the axial compressive stress of the edge strips;
And step seven, calculating the thickness of the girder web plate according to the shearing force of the girder section.
In a preferred embodiment of the present application, the fuselage is given a uniformly distributed load bearing structure as shown in fig. 3, L1 and L2 being the distances between the study stringers and their left and right side stringers, respectively. In the first step, uniformly distributed loads born by the longitudinal beams are calculated. The size and the distribution of the uniformly distributed load born by the longitudinal beam are calculated by bearing the load of the uniformly distributed surface by the wall plates on the two sides of the longitudinal beam, namely:
the uniformly distributed load born by the longitudinal beam is as follows:
q＝p*Δl
Wherein q is the uniform load born by the longitudinal beam, p is the uniform surface load born by the wall plates at two sides of the longitudinal beam, and Deltal is the width of the wall plates at two sides of the longitudinal beam.
Further, in the second step, the shearing force and the bending moment of the longitudinal beam section are calculated, and the shearing force distribution and the bending moment distribution of the longitudinal beam section are calculated according to the uniformly distributed load born by the longitudinal beam, as shown in figures 4-5, wherein,
The shear force of the profile of the longitudinal beam is calculated according to the uniformly distributed load born by the longitudinal beam, and is as follows:
the bending moment of the profile of the longitudinal beam is calculated according to the uniformly distributed load born by the longitudinal beam, and is as follows:
wherein Q x is the shear force of the profile of the longitudinal beam, M x is the bending moment of the profile of the longitudinal beam, and x is the distance from any point to the starting point by taking one end of the longitudinal beam as the starting point.
Then, in the third step, the neutral axis position of the longitudinal beam along the length direction, namely the neutral layer position of the longitudinal beam, is calculated, and in the embodiment, the method is mainly applied to preliminary design of rigidity strength of the longitudinal beam, so that the rigidity influence of a web plate of the beam is ignored when the neutral layer of the I-beam is calculated, and the upper edge strip and the lower edge strip of the longitudinal beam are mainly considered when the I-beam is calculated;
The neutral layer position of the stringers is:
Wherein H is the neutral layer position of the longitudinal beam, a is the area of the upper edge strip of the longitudinal beam, b is the area of the lower edge strip of the longitudinal beam, and H is the height of the longitudinal beam.
In the fourth step, bending moment of inertia I of the section of the longitudinal beam is calculated, a web plate of the longitudinal beam is not considered when the bending moment of inertia of the section is calculated, and the web plate is considered to bear shear load mainly;
The bending moment of inertia of the stringer profile is:
I＝a(H-h)2+bh2
wherein I is the bending moment of inertia of the cross section of the longitudinal beam.
And in the fifth step, calculating the maximum axial tensile stress of the edge strip of the longitudinal beam which is subjected to stretching and the axial compressive stress of the edge strip of the longitudinal beam which is subjected to compression. Calculating the maximum stress of the longitudinal beam stretched edge strip through a bending stress calculation formula, and calculating the axial stress of the compressed edge strip according to the corresponding relation between the bending moment and the force arm; wherein,
The maximum axial tensile stress of the edge strip of the longitudinal beam which bears the tension is as follows:
The axial compressive stress of the edge strip of the longitudinal beam bearing compression is as follows:
Wherein σ t is the maximum axial tensile stress of the cap and σ c is the axial compressive stress of the cap.
And step six, calculating the areas of the upper edge strip and the lower edge strip of the longitudinal beam. And (3) the size of the arrangement area of the upper and lower edge strips of the longitudinal beam can be obtained by utilizing matlab to carry out five-two combined solution on the steps.
The area of the upper edge strip of the longitudinal beam is as follows:
the area of the longitudinal beam lower edge strip is as follows:
and finally, in the step seven, the thickness of the girder web plate is calculated according to the shearing force of the girder section, and the cell size of the girder web plate is calculated. The web thickness profile may be analytically calculated based on shear stability control. The relation between the profile stress of the longitudinal beam web and the web thickness and the size is as follows:
Wherein τ cr is shear instability stress of a longitudinal beam web, K s is boundary support coefficient of the longitudinal beam web, E is elastic modulus of the material, mu is Poisson's ratio of the material, and t is thickness of the longitudinal beam web.
The design method of the I-shaped longitudinal beam for bearing the uniform load is based on the principle that the variable-section I-shaped longitudinal beam bears the uniform load, the relation between the section stress distribution and the section parameters of the longitudinal beam is determined by gradual analysis and calculation, and the design method of the I-shaped longitudinal beam for bearing the uniform load is provided through stress control.
The foregoing is merely illustrative of the present application, and the present application is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present application should be included in the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (8)
1. The design method of the I-shaped longitudinal beam for bearing uniformly distributed loads is characterized by comprising the following steps of:
Step one, calculating uniform load born by a longitudinal beam;
step two, calculating the shearing force and bending moment of the profile of the longitudinal beam according to the uniformly distributed load born by the longitudinal beam;
step three, calculating the neutral layer position of the longitudinal beam;
step four, calculating bending moment of inertia of the longitudinal beam section;
calculating the maximum axial tensile stress of the edge strips of the longitudinal beams subjected to stretching and the axial compressive stress of the edge strips of the longitudinal beams subjected to compression;
step six, calculating the areas of the upper and lower edge strips of the longitudinal beam according to the maximum axial tensile stress and the axial compressive stress of the edge strips;
And step seven, calculating the thickness of the girder web plate according to the shearing force of the girder section.
2. The method for designing an i-shaped longitudinal beam for supporting uniform load according to claim 1, wherein in the first step, the calculating the uniform load supported by the longitudinal beam comprises:
the uniformly distributed load born by the longitudinal beam is as follows:
q＝p*Δl
Wherein q is the uniform load born by the longitudinal beam, p is the uniform surface load born by the wall plates at two sides of the longitudinal beam, and Deltal is the width of the wall plates at two sides of the longitudinal beam.
3. The method for designing an i-shaped longitudinal beam for bearing uniform load according to claim 2, wherein in the second step, the calculating the shearing force and the bending moment of the section of the longitudinal beam according to the uniform load bearing by the longitudinal beam comprises:
the shear force of the profile of the longitudinal beam is calculated according to the uniformly distributed load born by the longitudinal beam, and is as follows:
the bending moment of the profile of the longitudinal beam is calculated according to the uniformly distributed load born by the longitudinal beam, and is as follows:
wherein Q x is the shear force of the profile of the longitudinal beam, M x is the bending moment of the profile of the longitudinal beam, and x is the distance from any point to the starting point by taking one end of the longitudinal beam as the starting point.
4. The method for designing an i-beam for receiving uniform load according to claim 3, wherein in step three, the calculating the neutral layer position of the beam comprises:
the neutral layer position of the longitudinal beam is:
Wherein H is the neutral layer position of the longitudinal beam, a is the area of the upper edge strip of the longitudinal beam, b is the area of the lower edge strip of the longitudinal beam, and H is the height of the longitudinal beam.
5. The method for designing an i-beam for receiving uniform load according to claim 4, wherein in the fourth step, the calculating a bending moment of inertia of a beam section includes:
the bending moment of inertia of the longitudinal beam profile is:
I＝a(H-h)2+bh2
wherein I is the bending moment of inertia of the cross section of the longitudinal beam.
6. The method for designing an i-beam with uniformly distributed load according to claim 5, wherein in the fifth step, calculating the maximum axial tensile stress of the edge strip with the longitudinal beam subjected to the stretching and the axial compressive stress of the edge strip with the longitudinal beam subjected to the compression includes:
The maximum axial tensile stress of the edge strip of the longitudinal beam which bears the tension is as follows:
The axial compressive stress of the edge strip of the longitudinal beam bearing compression is as follows:
Wherein σ t is the maximum axial tensile stress of the cap and σ c is the axial compressive stress of the cap.
7. The method for designing an i-shaped longitudinal beam for bearing uniform load according to claim 6, wherein in the sixth step, a maximum axial tensile stress formula and an axial compressive stress formula of the edge strip are solved in a combined manner, so that the area of the upper edge strip of the longitudinal beam is:
the area of the longitudinal beam lower edge strip is as follows:
8. The method for designing an i-beam for receiving uniform load according to claim 7, wherein in step seven, the calculating the thickness of the beam web according to the shearing force of the beam profile comprises:
the thickness of the stringer web is determined according to the following formula:
Wherein τ cr is shear instability stress of a longitudinal beam web, K s is boundary support coefficient of the longitudinal beam web, E is elastic modulus of the material, mu is Poisson's ratio of the material, and t is thickness of the longitudinal beam web.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311796019.7A CN117951804A (en) | 2023-12-25 | 2023-12-25 | I-shaped longitudinal beam design method for bearing uniformly distributed load |
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| CN202311796019.7A CN117951804A (en) | 2023-12-25 | 2023-12-25 | I-shaped longitudinal beam design method for bearing uniformly distributed load |
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