CN113550437B - Evacuation Kaiwaite pyramid system double-layer spherical shell structure and evacuation method - Google Patents
Evacuation Kaiwaite pyramid system double-layer spherical shell structure and evacuation method Download PDFInfo
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Abstract
The invention discloses a vacuumizing Kaiwaite pyramid system double-layer spherical shell structure and a vacuumizing method, wherein an upper chord grid is a conventional Kaiwaite grid, the normal line of each corner point of each triangle of a lower chord grid passes through the gravity center position of one triangle of the upper chord grid, a triangular vacuumizing area of the upper chord grid is firstly calculated, the corner point of the triangle of the lower chord grid corresponding to the triangle gravity center of the vacuumizing area is a lower chord pyramid node of the vacuumizing area, and three web members and six lower chord members connected with the lower chord pyramid node of each vacuumizing area are vacuumized, so that the vacuumizing Kaiwaite pyramid system double-layer spherical shell structure is formed.
Description
Technical Field
The invention belongs to the field of large-span space structures, and particularly relates to a double-layer spherical shell structure of an evacuated Kaiwaite pyramid system for a large-span space and an evacuation method.
Background
The Kaiwate spherical shell is created in 1925 by Kaiwate of American engineer in order to improve the uneven size of grids in Schwedler type and combined square type spherical shells, the spherical shell structure has excellent stress performance, particularly has good performance under the action of earthquake and strong wind, and the American New Orleans super dome built in 1973 adopts the grid form, has the diameter of 213m and the rise of 32m, and keeps the maximum span record of the spherical shell structure for many years.
The conventional Kaiwaite spherical shell is characterized in that n (n is 6,8 and 12 … …) through long radial rods divide a spherical surface into n symmetrical fan-shaped curved surfaces, then the curved surfaces are divided into triangular meshes with relatively uniform sizes in each fan-shaped curved surface by a weft rod and an oblique rod, and left and right oblique rods in each fan-shaped surface are parallel, so that the spherical shell is also called as a parallel connected square spherical shell. The grid division form ensures that the grid size is uniform, the internal force is uniformly distributed, and the grid division form is commonly used for large-span and medium-span spherical shell structures.
Because the double-layer spherical shell of the Kaiwait type pyramid system consists of the triangular cones in space, the whole rigidity is very high, the rod pieces have certain redundancy, the mechanical properties of a plurality of rod pieces cannot be fully utilized, and the structure has further optimized space.
Disclosure of Invention
The invention aims to provide an evacuated double-layer spherical shell structure of a Kaiwait pyramid system and an evacuation method, aiming at the defects of the prior art, wherein a local web member and a lower chord member of the double-layer spherical shell of the Kaiwait pyramid system are extracted, so that the redundancy of the members is reduced, the mechanical property of the structural members is fully exerted, and the steel consumption of the double-layer spherical shell structure of the Kaiwait pyramid system is reduced.
In order to realize the purpose, the technical scheme of the invention is as follows:
a double-layer spherical shell structure of an evacuated Kaiwaite pyramid system comprises an upper chord spherical shell layer, a web member and a lower chord spherical shell layer, wherein the web member is connected with the upper chord spherical shell layer and the lower chord spherical shell layer; dividing the fan-shaped curved surface into triangular meshes by a warp rod, a weft rod and an oblique rod in each fan-shaped curved surface of each spherical shell layer, wherein the warp rod, the weft rod and the oblique rod of the upper chord spherical shell layer are upper chord members, the warp rod, the weft rod and the oblique rod of the lower chord spherical shell layer are lower chord members, the normal line of the angular point of each triangle of the lower chord spherical shell layer passes through the gravity center position of the triangle of the upper chord spherical shell layer, and the three angular points of the triangle of the upper chord spherical shell layer are connected with the angular point of the triangle of the lower chord spherical shell layer corresponding to the gravity center of the triangle of the upper chord spherical shell layer to form a web member; the upper chord spherical shell layer comprises a triangular evacuation area, and an evacuation area web member and an evacuation area lower chord member which are connected with the triangular corner point of the lower chord spherical shell layer and correspond to the gravity center of the evacuation area are evacuated.
Further, the upper chord spherical shell layer is of a complete Kaiwaite grid spherical shell structure.
Furthermore, the evacuation area is a plurality of independent triangles; the evacuated region is provided with corresponding evacuated region lower chord pyramid nodes, evacuated region web members and evacuated region lower chord members; the evacuated area lower chord pyramid node is one angular point of a lower chord spherical shell layer triangle, the normal line of the evacuated area lower chord pyramid node passes through the gravity center of the evacuated area, the evacuated area lower chord pyramid node is connected with three angular points of the evacuated area to form an evacuated area web member, and the evacuated area web member and the evacuated area lower chord member are connected with the evacuated area lower chord pyramid node.
Further, the lower chord spherical shell layer is formed by an evacuated area web member and an evacuated area lower chord member which are connected with an evacuated area lower chord pyramid node corresponding to the evacuated area.
The method for evacuating the Kawiter pyramid system double-layer spherical shell structure comprises the following steps of:
step one, determining a triangular evacuated area:
the evacuation area is determined according to an upper chord spherical shell layer grid of a double-layer spherical shell of a conventional Kaiwaite pyramid system, the upper chord spherical shell layer grid is set to have n circles from the center of a circle to the outside, the evacuation area is distributed in the 2m +1 (odd number circles) circle of each sector at intervals, wherein m is an integer and meets the following conditions: m is more than or equal to 1 and less than or equal to 0.5 (n-1), the number of the evacuation areas of each sector in the 2m +1 th circle is m independent triangles, the m independent triangles are arranged at intervals, the number of the evacuation areas in the 2m +1 th circle is m × K for the whole structure, and K is an upper chord spherical shell layer sector curved surface, wherein K is 6,8,12 …;
step two, determining a lower chord pyramid node of the evacuated region:
after the evacuated area is determined, determining the angular point of a lower chord triangle corresponding to the gravity center of the triangle of the evacuated area, wherein the normal line of the angular point of the lower chord triangle passes through the gravity center of the triangle of the evacuated area, and the angular point of the lower chord triangle is the lower chord pyramid node of the evacuated area; the lower chord pyramid node of the evacuated area is provided with an upper chord triangle corresponding to the lower chord pyramid node, namely the evacuated area, and the lower chord pyramid node of the evacuated area is connected with three angular points of the evacuated area to form three web members, namely three evacuated area web members; in the lower chord triangular grid, one lower chord pyramid node is simultaneously connected with six lower chords, and the six lower chords connected with the lower chord pyramid node of the evacuated area are the six evacuated area lower chords;
and thirdly, three evacuation area web members and six evacuation area lower chord members connected with the evacuation area lower chord pyramid node corresponding to each evacuation area are evacuated to form an evacuated Kevlar system double-layer spherical shell structure.
The invention has the beneficial effects that:
after the evacuation of the double-layer spherical shell structure of the Kaiwait pyramid system is adopted, the redundancy of the rod pieces is reduced, and the mechanical property of the structural rod pieces is fully exerted, so that the steel consumption of the double-layer spherical shell structure of the Kaiwait pyramid system is reduced.
After the evacuated double-layer spherical shell structure of the Kaiwaite pyramid system is adopted, the deflection of the structural mid-span is not obviously increased, the requirement of the specification on mid-span deformation is met, the steel consumption is reduced by about 20 percent compared with the conventional double-layer spherical shell structure scheme of the Kaiwaite pyramid system, and the evacuated double-layer spherical shell structure has good economic benefit.
Drawings
FIG. 1 is a top view of a double-layered spherical shell of a Kaiwait pyramid system before evacuation according to the present invention
FIG. 2 is a schematic axial view of a double-layer spherical shell junction of a Kaiwait pyramid system before evacuation according to the present invention
FIG. 3 plan view of an evacuated area according to the invention
FIG. 4 is a side view of the evacuated region of the present invention
FIG. 5 is a partial enlarged view of an evacuated region of the present invention
FIG. 6 is a top view of a double-layered spherical shell of an evacuated Kaiwait pyramid system of the present invention
FIG. 7 is a schematic axial view of a double-layer spherical shell structure of a Kaiwait pyramid system after evacuation according to the present invention
FIG. 8 is an enlarged view of a portion of the invention after evacuation
FIG. 9 is the calculation of stress ratio for a non-evacuated Kaiwait grid
FIG. 10 shows the calculation of the stress ratio of the Kaiwait net frame after evacuation
FIG. 11 shows the calculation results of the amount of steel for the non-evacuated Kaiwait net frame
FIG. 12 shows the calculation results of the steel amount for the Kaiwait net rack after evacuation
In the figure, 1-upper chord (indicated by thick solid line in the figure), 2-web member (indicated by broken line in the figure), 3-lower chord (indicated by thin solid line in the figure), 4-evacuation area (indicated by filled triangle), 5-evacuation area lower chord pyramid node, 6-evacuation area web member and 7-evacuation area lower chord member.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described with reference to the accompanying drawings.
The invention is illustrated by a schematic diagram of a double-layer spherical shell structure of a Kaiwet pyramid system of K6 type (6 symmetrical fan-shaped curved surfaces), and the Kaiwet grids of the other types of K8 and K12 … (8 symmetrical fan-shaped curved surfaces and 12 symmetrical fan-shaped curved surfaces …) are similar to the K6 type, which is not repeated herein.
In the present embodiment, as shown in fig. 1, the hemispherical kaiwate pyramid double-layer spherical shell includes an outer spherical shell and an inner spherical shell.
Each spherical shell is divided into six symmetrical fan-shaped curved surfaces by six through long warp rods, each fan-shaped curved surface is divided into triangular meshes with symmetrical sizes by a latitudinal rod and an oblique rod, the intersection points of the meshes are angular points of the triangles, and the warp rods, the latitudinal rods and the oblique rods of each spherical surface form the meshes; the diagonal rods comprise a plurality of left diagonal rods and right diagonal rods, and the rod pieces are connected with each other to form an integral structure.
As shown in fig. 1, in each sector curved surface, an oblique rod is led out from the intersection point of each warp rod and each weft rod, namely a left oblique rod and a right oblique rod, one end of each oblique rod is led out from the intersection point of each warp rod and each weft rod, the other end of each oblique rod is arranged on the weft rod at the bottommost layer, each left oblique rod and each right oblique rod respectively have an intersection point, and the intersection point is arranged on the weft rod at the bottommost layer; the left diagonal rods in each sector-shaped curved surface are all parallel to each other, and the right diagonal rods in each sector-shaped curved surface are all parallel to each other.
In fig. 1, the latitudinal rods divide the hemispherical kaiwait pyramid spherical shell into 12 circles, the first circle is formed by the hexagonal latitudinal rods, and the other 11 circles are formed by the circular latitudinal rods;
the outer spherical shell is called an upper chord spherical shell layer, and the grid formed by the upper chord spherical shell layer is an upper chord grid; the inner layer spherical shell is called as a lower chord spherical shell layer, and the grid formed by the lower chord spherical shell layer is a lower chord grid.
All the rods of the upper chord grid are called upper chords 1; all the rods of the lower chord mesh are called lower chords 3.
The member connecting the upper chord grid and the lower chord grid is a web member 2.
The arrangement mode of the upper chord grids and the lower chord grids is as follows: the upper chord grids are conventional Kaiwate grids, the normal of the intersection point of the lower chord grids passes through the gravity center position of the triangles of the upper chord grids, and the intersection point of the grids is the angular point of each triangle, so that the normal of each angular point of each triangle of the lower chord grids passes through the gravity center position of one of the triangles of the upper chord grids, namely, each angular point of the triangle of the lower chord grids corresponds to the gravity center of one of the triangles of the upper chord grids.
The upper chord grid triangle is called an upper chord triangle, and the lower chord grid triangle is called a lower chord triangle.
And one angular point of the lower chord triangle is provided with an upper chord triangle corresponding to the angular point, the normal line of the angular point of the lower chord triangle passes through the gravity center of the upper chord triangle, the angular point of the lower chord triangle corresponds to the gravity center of the upper chord triangle, in this case, the angular point of the lower chord triangle is connected with three angular points of the upper chord triangle corresponding to the angular point of the lower chord triangle, and the formed connecting rod is the web member 2.
One corner point of the lower chord triangle is simultaneously connected with three corner points of the upper chord triangle corresponding to the lower chord triangle to form a triangular pyramid-shaped tetrahedral structure, the web member 2 is a prism of the tetrahedral structure, and the vertex of the triangular pyramid is one corner point of the lower chord triangle.
The web members 2 are led out from three angular points of each triangle of the upper chord grid, the angular points of the lower chord triangle corresponding to the gravity center of the upper chord triangle are connected, the angular points are the lower chord pyramid nodes, a triangular pyramid space structure is formed, and the double-layer spherical shell of the hemispherical Kaiwaite pyramid system is better in overall stress performance due to the space structure of the triangular pyramid.
In the lower chord triangular mesh, one lower chord pyramid node is simultaneously connected with six lower chords 3.
As shown in fig. 1 and 2, the evacuated fore kawait pyramid system double-layer spherical shell structure comprises an upper chord member 1, a web member 2 and a lower chord member 3.
As shown in fig. 3 and 4, the evacuated region 4 is determined according to the upper chord grid of the double-layer spherical shell of the kaiwate pyramid system, assuming that the upper chord grid is n circles outwards from the center of the circle, the evacuated region 4 is distributed in the 2m +1 (odd circles) of each sector at intervals, where m is an integer and satisfies the following conditions: m is more than or equal to 1 and less than or equal to 0.5 (n-1), the number of the evacuated areas 4 in the circle 2m +1 of each sector is m, the number of the evacuated areas in the invention refers to m independent triangles, the m independent triangles are arranged at the circle 2m +1 of the upper chord grid at intervals, the number of the evacuated areas 4 in the circle 2m +1 for the whole structure is m, and K is 6,8,12 ….
In the invention, the evacuation method comprises the following steps: firstly, determining an evacuated area through calculation, wherein the angular point of a lower chord triangle corresponding to the gravity center of each single triangle in the evacuated area is an evacuated lower chord pyramid node 5, and removing three evacuated area web members 6 and six evacuated area lower chord members 7 connected with the evacuated area lower chord pyramid node 5.
As shown in fig. 5, each individual evacuated region 4 comprises an upper chord 1, a web 2, a lower chord 3, an evacuated region lower chord pyramid node 5, an evacuated region web 6, and an evacuated region lower chord 7.
The specific extraction method is shown in fig. 3 to 8:
firstly, determining a triangular evacuated region 4 by the above calculation method, wherein in fig. 3 and 4, the evacuated region 4 is marked by a shadow in an upper chord grid, and the evacuated region 4 is triangular;
secondly, determining a lower chord pyramid node 5 of the evacuated region, and determining an angular point of a lower chord triangle corresponding to the gravity center of a triangle of the evacuated region 4 after the evacuated region 4 is determined, wherein the normal line of the angular point of the lower chord triangle passes through the gravity center of the triangle of the evacuated region 4, and the angular point of the lower chord triangle is the lower chord pyramid node 5 of the evacuated region; the lower chord pyramid node 5 of the evacuated region is provided with an upper chord triangle corresponding to the node, namely the evacuated region 4, the lower chord pyramid node 5 of the evacuated region is connected with three angular points of the evacuated region 4 to form three web members, and the three web members are three evacuated region web members 6; in the lower chord triangular grid, one lower chord pyramid node is simultaneously connected with six lower chords, and the six lower chords connected with the lower chord pyramid node 5 of the evacuated area are six evacuated area lower chords 7;
finally, three evacuation zone web members 6 and six evacuation zone lower chords 7 connected with the evacuation zone lower chord pyramid node 5 corresponding to each evacuation zone 4 are evacuated, so that an evacuated kawitter pyramid system double-layer spherical shell structure as shown in fig. 6-8 is formed.
Through finite element software analysis and calculation, the conditions set by the software calculation are as follows: constant load of a Kaiwait pyramid system double-layer spherical shell structure: 0.5kn/m 2 (ii) a Live loading: 0.5kn/m 2 (ii) a Basic wind pressure: 0.3kpa (50 year one encounter); temperature load: the upper temperature difference is +25 degrees, and the lower temperature difference is: -30 °; the diameter of a double-layer spherical shell of the Kaiwaite pyramid system is set to be 48 m; fig. 9 and 10 are the calculation results of the stress ratio of the kevlar net frame after non-evacuation and evacuation respectively, the stress ratio of the kevlar net frame after non-evacuation is 0.86, and the stress ratio of the kevlar net frame after evacuation is 0.82; the results of the calculation of the steel amounts for the kevlar net frames in fig. 11 and 12, which were not evacuated and after evacuation, respectively, showed by software calculation that the steel amount for the 48m diameter non-evacuated kevlar net frame was 88.35t, the steel amount for the 48m diameter evacuated kevlar net frame was 70.20t, and the steel amount after evacuation was saved by 20.5%.
After the evacuation Kaiwaite pyramid system double-layer spherical shell structure is adopted, the redundancy of the rod pieces is reduced, and the mechanical property of the structural rod pieces is fully exerted, so that the steel consumption of the Kaiwaite pyramid system double-layer spherical shell structure is reduced, according to the analysis and calculation of finite element software, after the evacuation Kaiwaite pyramid system double-layer spherical shell structure is adopted, the deflection of the structure mid-span is not obviously increased, the requirement of specification on mid-span deformation is met, the steel consumption is reduced by about 20 percent compared with the conventional Kaiwaite pyramid system double-layer spherical shell structure scheme, and the evacuation Kaiwaite pyramid system double-layer spherical shell structure has good economic benefit.
Finally, it should be noted that: while the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to one skilled in the art that various changes in the form and details may be made therein without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A vacuumizing Kaiwaite pyramid system double-layer spherical shell structure comprises an upper chord spherical shell layer, a web member (2) and a lower chord spherical shell layer, wherein the web member (2) is connected with the upper chord spherical shell layer and the lower chord spherical shell layer; each fan-shaped curved surface of each spherical shell layer is divided into triangular meshes by a warp rod, a weft rod and an oblique rod, the warp rod, the weft rod and the oblique rod of the upper chord spherical shell layer are upper chord members (1), and the warp rod, the weft rod and the oblique rod of the lower chord spherical shell layer are lower chord members (3), and the spherical shell is characterized in that the normal line of the angular point of each triangle of the lower chord spherical shell layer passes through the gravity center position of the triangle of the upper chord spherical shell layer, and the three angular points of the triangle of the upper chord spherical shell layer are connected with the angular point of the triangle of the lower chord spherical shell layer corresponding to the gravity center of the triangle of the upper chord spherical shell layer to form a web member (2); the upper chord spherical shell layer comprises a triangular evacuated region (4), and an evacuated region web member (6) and an evacuated region lower chord member (7) which are connected with a triangular angular point of the lower chord spherical shell layer and correspond to the gravity center of the evacuated region (4) are evacuated;
the evacuation area (4) is triangular; the evacuated region (4) is provided with a corresponding evacuated region lower chord pyramid node (5), an evacuated region web member (6) and an evacuated region lower chord member (7); the evacuated area lower chord pyramid node (5) is an angular point of a lower chord spherical shell layer triangle, the normal of the evacuated area lower chord pyramid node (5) passes through the gravity center of the evacuated area (4), the evacuated area lower chord pyramid node (5) is connected with three angular points of the evacuated area (4) to form an evacuated area web member (6), and the evacuated area web member (6) and the evacuated area lower chord member (7) are both connected with the evacuated area lower chord pyramid node (5).
2. The evacuated kawait pyramid system double-layer spherical shell structure of claim 1, wherein the upper chord spherical shell layer is a complete kawait lattice spherical shell structure.
3. The evacuated kawitter pyramid system double-layer spherical shell structure according to claim 1, wherein the lower chord spherical shell layer is formed by an evacuated region web member (6) and an evacuated region lower chord member (7) which are connected with an evacuated region lower chord pyramid node (5) corresponding to the evacuated region (4).
4. The method of evacuating a double-layered spherical shell structure of the kevlar pyramid system according to claim 1, comprising the steps of:
step one, determining a triangular evacuation area (4):
the evacuation area (4) is determined according to an upper chord spherical shell layer grid of a double-layer spherical shell of a conventional Kaiwert pyramid system, the upper chord spherical shell layer grid is set to be n circles from the center of a circle to the outside, the evacuation area is distributed in the 2m +1 circle (odd circles) of each sector at intervals, m is an integer and meets the following conditions: m is more than or equal to 1 and less than or equal to 0.5 (n-1), the number of the evacuation areas (4) of each sector in the 2m +1 th circle is m independent triangles, the m independent triangles are arranged at intervals, the number of the evacuation areas in the 2m +1 th circle is m K for the whole structure, and K is an upper chord spherical shell layer sector curved surface, wherein K is 6,8,12 …;
step two, determining a lower chord pyramid node (5) of the evacuation area:
after the evacuated region (4) is determined, determining the corner point of a lower chord triangle corresponding to the gravity center of the triangle in the evacuated region (4), wherein the normal line of the corner point of the lower chord triangle passes through the gravity center of the triangle in the evacuated region (4), and the corner point of the lower chord triangle is the lower chord pyramid node (5) of the evacuated region;
the lower chord pyramid node (5) of the evacuated region is provided with an upper chord triangle corresponding to the lower chord pyramid node, namely the evacuated region (4), the lower chord pyramid node (5) of the evacuated region is connected with three angular points of the evacuated region (4) to form three web members, namely three evacuated region web members (6); in the lower chord triangular grid, one lower chord pyramid node is simultaneously connected with six lower chords, and the six lower chords connected with the lower chord pyramid node (5) of the evacuated area are six evacuated area lower chords (7);
and thirdly, three evacuation area web members (6) and six evacuation area lower chords (7) connected with the evacuation area lower chord pyramid node (5) corresponding to each evacuation area (4) are evacuated to form an evacuated Kawitt pyramid system double-layer spherical shell structure.
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| EP2123836A1 (en) * | 2008-05-19 | 2009-11-25 | Technische Universität Wien | Method for manufacturing a shell |
| CN106592769A (en) * | 2016-12-12 | 2017-04-26 | 武汉大学 | Double-layer spherical reticulated shell structure modeling method and structural form |
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