JPH07216990A - Method for forming spherical lattice shell of single layer - Google Patents

Abstract

PURPOSE:To promote efficiency of fabrication and assembling by a method wherein a circle, as a plan view of a semispherical dome, is divided into sectors and each of the sides thereof is divided into equal parts so that a network pattern including almost regular triangles each having a side equal to the divided part constitutes a spherical lattice shell. CONSTITUTION:A circle 1, as a plan view of a semispherical dome, is divided from the center T thereof into sectors 2 and a side of the sector (radius) is divided into several equal parts (e.g. five parts). Next, an equilateral triangle TA1B1 is formed from lattice members. The triangle should be formed into a regular triangle as far as possible. The second layer and following layers of lattice are formed in the similar manner. And lattice members for a segment portion 16 are formed separately. Hence distribution of rigidity of a dome is made uniform and isotropy thereof can be nearly achieved so that kinds of lattice members can be reduced. As a result, fabrication and assembling can be easily performed, thereby reducing costs.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention is carried out in constructing a dome roof of a pillarless building such as a gymnasium and a cultural center, and in particular, a method of constructing a hemispherical dome roof with a spherical lattice shell by a set of isosceles triangles. Regarding

[0002]

2. Description of the Related Art In constructing a hemispherical dome roof with spherical lattice shells, considering the buckling safety of the entire spherical lattice shell structure, the uniformity of member stress, etc., the lattice members are arranged in a grid pattern in three directions. That is, a method of arranging the triangular network pattern on the spherical surface is rational, but in this case, from the viewpoint of labor saving and cost reduction of the production of the lattice member, the lattice members should be as uniform in length and kind as possible. It is important to devise so that the number is reduced.

As a method of constructing a spherical lattice shell of a hemispherical dome, it is geometrically difficult to construct an equilateral triangle with lattice members having the same length. Therefore, conventionally, an improved method of constructing a spherical lattice shell with an equilateral triangle as uniform as possible has been described, for example, in the Architectural Institute of Japan held in Hokkaido in August 1986, "Frame analysis regarding buckling of single-layer rigid-contact lattice shells. On the compatibility of shell analysis ”.

As shown in FIG. 2 and FIG. 3, the contents of the above research are as follows. First, a fan-shaped main dividing line A and B obtained by dividing a circle 1 in which a hemispherical dome is viewed in plan into six equal parts is divided into N equal parts. Then, make an isosceles triangle ΔTA ₁ B ₁ on the top. Next, a curve at which the plane formed by the dividing center D and the equal points A ₂ and B ₂ intersects the spherical surface is obtained, and the bisector of the curve is set as the node C ₂ . Similarly, a curve at which the plane formed by the dividing center D and the equally divided points A _N and B _N intersects with the spherical surface is obtained, and the N equally divided points of the same curve are set as the nodes C _N. The split circle portion remaining outside the chord A _N −B _{N of the} fan shape is provided with virtual equal points A _{N + 1} and B _{N + 1} on the extension of the hypotenuses T−A _N and T−B _N. A curve that intersects the plane formed by this and the dividing center D and the virtual spherical surface is obtained, and N + 1 of this curve
_{Let the} equal points be virtual nodes C _{N + 1} . The virtual node C _{N + 1}
And the intersection of the curve A _N B _N and the curve connecting the corresponding node C _N at the shortest distance on the spherical surface is the outermost node. The dividing center D is the intersection of the central axis OO ′ of the spherical surface and the plane formed by the virtual equal points A _{N + 1} and B _{N + 1} and the midpoint C of the arc A _N B _N.

[0005]

In the method of forming a triangle network pattern by dividing an arc passing through the apex of a hemisphere into six equal parts as in the above-mentioned conventional method, the length of the base of the formed triangle is equal for each layer. However, the length of the hypotenuse cannot be unified. For example, for an isosceles triangle ΔTA _N B _N from the apex of a fan to a chord, when the main dividing lines A and B of the fan are divided into 5 equal parts (when N = 5), 16 types are divided into 10 equal parts. In the case (N = 10), the spherical lattice shell is configured by a triangular network pattern in which 51 types of lattice members are combined. Therefore, even if it is a method of configuring with a uniform triangle network pattern as much as possible, it can not be denied that there are still too many types of lattice members to be manufactured, and it takes a lot of time and effort to manufacture and combine the lattice members. Assembling cost also increases.

Therefore, it is an object of the present invention to construct a hemispherical dome by constructing a single-layer spherical lattice shell with a much smaller number of triangular network patterns, thereby significantly reducing the number of lattice member manufacturing and assembly steps. , A method of constructing a single-layer spherical lattice shell capable of further saving labor and cost.

[0007]

As a means for solving the above-mentioned problems of the prior art, the method for constructing a single-layer spherical lattice shell according to the present invention uses a circle 1 in which a hemispherical dome is viewed in plan as much as possible. The apex angle θ is defined as the internal angle of the sector 2 divided into equal parts so that the rigidity distribution becomes uniform and is as close to isotropic as possible, that is, each triangle is as close to an equilateral triangle as possible. The two main dividing lines A and B on the sphere, which are the hypotenuses of 2, are obtained by dividing each of the two main dividing lines A and B into several equal parts, and the first dividing lines A ₁ and One isosceles triangle 4 formed by the base 3 connecting B ₁ is made of lattice members.

Next, an isosceles triangle 4a equivalent to that obtained by rotating the isosceles triangle 4 about its base 3 by about 180 degrees is formed by a lattice member on the spherical surface, and further the second layer on the main dividing line is formed. Two isosceles triangles 7 and 7 having a base 6 as a line segment connecting the equally divided points A ₂ and B ₂ and the vertex 14 of the rotated isosceles triangle are made of lattice members, respectively, and then the two two isosceles triangles are formed. Approximately 18 equilateral triangles 7 and 7 with each base 6 as the axis of rotation
0 degree rotation is equal isosceles 7a to was, 7a and made in lattice member on a spherical surface, two isosceles triangles that are further said rotation equal point A _3, B ₃ of the third layer of the main dividing line The three isosceles triangles 11, 11 and 12 having bases 9, 9 and 10 connecting the respective vertices 15 and 15 are made of lattice members respectively, and the same procedure is followed for the bottom layer on the main dividing line. It is characterized in that the spherical surface is constituted by spherical lattice shells of a triangular network pattern repeatedly until reaching A _N B _N.

The present invention also comprises triangular spherical lattice shells up to the lowermost layer A _N -B _N on the main dividing line of the sector 2 obtained by dividing the circle 1 into several parts, and the remaining split circle portion 16 has the lowermost layer A. _N- B _N each lattice member and ring column position 17 ...
Another feature is that a triangle is formed by.

[0010]

The length of the base of the isosceles triangle serving as the axis of rotation is slightly different for each layer, but the length of the hypotenuse is the same. Therefore, the isosceles triangle TA _N B _N excluding the fan-shaped split circle portion 16
, The main dividing lines T-A and T-B are 5 respectively.
The spherical lattice shells can be configured with a triangular network pattern in which 10 types of lattice parts are combined (when N = 5) and 10 types of regions are divided (when N = 10) and 31 types of lattice members are combined.

[0011]

EXAMPLE An example of the present invention shown in FIG. 1 will be described below. FIG. 1 shows a triangular network pattern up to the position of a chord A ₅ -B ₅ of a sector 2 having an internal angle θ of 60 degrees (hereinafter referred to as the lowermost layer) obtained by dividing a circle 1 in which a hemispherical dome is viewed in plan into 6 equal parts. It shows a skeleton composed of. The reason why the circle 1 is divided into six equal sectors with an interior angle of 60 degrees is that the rigidity distribution is as uniform as possible and is as close to isotropic as possible.
That is to make each triangle as close to an equilateral triangle as possible. As a method of constructing the spherical lattice shell of the triangular network pattern, the internal angle of the sector 2 is 60 degrees, and the two main dividing lines A and B on the spherical surface which is the hypotenuse of the sector 2 are divided into 5 equal parts. two oblique side up equally divided points a _1, B ₁ of the first layer was collected using T-a ₁ (=
5), T-B ₁ (= 5) and a base A ₁ -B ₁ (= 3) connecting the equal points A ₁ and B ₁ to each other, one isosceles triangle ΔTA ₁ B ₁ Make (= 4) with lattice members.

Next, an isosceles triangle 4a equivalent to the isosceles triangle 4 of the first layer rotated 180 + α degrees around the base 3 as a rotation axis is formed on the spherical surface by a lattice member. Further, a line segment connecting the apex 14 of the rotated isosceles triangle and the equally dividing points A ₂ and B ₂ of the second layer on the main dividing line is a base 6
The two isosceles triangles 7 and 7 are made of lattice members. The two isosceles triangles 7, 7 are congruent because the two sides have the same angle between them. Therefore, each corresponding base 6
Are equal in length. After all, the two isosceles triangles 4 and 4
The lengths of the hypotenuses 5 and 5 of a are the same, and the hypotenuses 8 and 5 of the two isosceles triangles 7 and 7 are also the same.
However, with the base 3 of the two isosceles triangles 4 and 4a,
The bases 6 of the two isosceles triangles 7, 7 have slightly different lengths. Therefore, there are three types of lattice members that form the above triangular network pattern (reference numerals 3 and 5 and 6).

Next, the two isosceles triangles 7, 7 of the second layer are rotated 180 + α degrees around the base 6 of each as an axis of rotation, and isosceles triangles 7a, 7a equivalent to the third layer are latticed on the spherical surface of the third layer. Made from materials. Further, line segments connecting the third-layer equidistant points A ₃ and B ₃ on the main dividing line and the vertices 15 and 15 of the two rotated isosceles triangles 7a and 7a are defined as bases 9 and 10. The three isosceles triangles 11 and 12 are made of lattice members. The two isosceles triangles 11 and 11 on both sides
Is congruent because the two sides and the angle between them are equal. Therefore, although the bases 9 and 9 have the same length, they are different from the base 10 of the remaining isosceles triangle 12. Also, the hypotenuses 5 of the three isosceles triangles 11, 11 and 12 of the third layer
The lengths of 8 and 13 are all the same. Therefore, there are five types of lattice members that form the above triangular network pattern (reference numerals 3 and 5, 6 and 9 and 10).

Hereinafter, the same procedure is repeated until the lowermost layer A ₅ -B ₅ (the position of the chord) on the main dividing line is reached, and the spherical surface is formed by a spherical lattice shell having a triangular network pattern. As a result, when the main dividing lines A and B are divided into 5 equal parts (when N = 5), a triangular network pattern up to the lowermost layer A ₅ -B ₅ of the sector 2 is formed by combining 10 types of lattice members. it can. Similarly, in the case of dividing into 10 equal parts (when N = 10), by combining 31 types of lattice members, the lowermost layer A ₅ -B ₅ of the sector 2 can be constituted by a spherical lattice shell having a triangular network pattern.

The split circle portion 16 remaining outside the lowermost layer A ₅ -B _{5 of} the fan-shaped portion 2 is formed into a triangular shape by each lattice member constituting the lowermost layer A ₅ -B ₅ and the ring column position 17 ... Finally, the whole part of the fan shape 2 can be composed of spherical lattice shells of a triangular network pattern to construct a hemispherical dome. In addition, when the structural performance of the triangular network pattern in which all the fan-shaped portions are formed of spherical lattice shells was investigated, it was revealed that the entire frame and the members have almost the same performance as the conventional method.

[0016]

According to the method for constructing a single-layer spherical lattice shell according to the present invention, when the main dividing line is divided into 5 equal parts, about 63% and 10 equal parts are divided from the conventional method. Can form an isosceles triangle portion excluding a fan-shaped split circle portion with 61% kinds of lattice members. Therefore, the number of steps for manufacturing and assembling the members is greatly reduced, and labor saving and cost reduction are achieved accordingly.

[Brief description of drawings]

FIG. 1 is a plan view showing a method for forming a single-layer spherical lattice shell.

FIG. 2 is a plan view showing a conventional example.

FIG. 3 is a front view showing a conventional example.

[Explanation of symbols]

1 circle 2 fan-shaped θ vertex angle A main dividing line B main dividing line 5 hypotenuse A ₁ equal point B ₁ equal point 3 base 4 isosceles triangle 4a isosceles triangle A ₂ equal point B ₂ equal point 14 vertex 6 base 7 isosceles 7a isosceles A ₃ equal parts the point B ₃ equal portions point 15 vertex 9 base 10 base 11 isosceles triangles 12 isosceles triangles A _N equally divided point B _N equally divided points 16 Warien portions 17 ring column position

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Shinzaburo Imamiya 18-22 Nishiki, Naka-ku, Aichi Prefecture Nagoya City Takenaka Corporation Nagoya Branch (72) Inventor Mutsuo Sahashi Naka City, Aichi Prefecture Naka-ku, Aichi Prefecture Nishiki 1-Chome 18-22 Co., Ltd. Takenaka Corporation Nagoya Branch (72) Inventor Hiroshi Soga Nishiki 1-Chome 18-22 Naka Naka Ward, Aichi Prefecture Takenaka Corporation Nagoya Branch

Claims (3)

[Claims] 1. A circle in which a hemispherical dome is viewed in plan view has a rigidity distribution as uniform as possible and is as close to isotropic as possible, that is, each triangle is as close to an equilateral triangle as possible. The apex angle is the interior angle of the fan divided into several parts,
Further, it is formed by two oblique lines of the first layer obtained by dividing each of the two main dividing lines on the spherical surface, which is the oblique side of the fan shape, into equal parts, and a base connecting the equally dividing points of the oblique sides. One isosceles triangle is made of lattice members, and then the isosceles triangle is rotated about 1 at its base.
An isosceles triangle equivalent to that rotated by 80 degrees is made of a lattice member on a spherical surface, and a line segment connecting the equal-division point of the second layer on the main dividing line and the vertex of the rotated isosceles triangle is defined as the base. Two isosceles triangles are each made of a lattice member, and then the above two isosceles triangles are each rotated about 180 degrees with each base as a rotation axis. Make three isosceles triangles whose bases are line segments that connect the equal points of the third layer on the main dividing line and the vertices of the two rotated isosceles triangles, respectively, using the lattice member. Is repeated until the lowermost layer on the main dividing line is reached, and the spherical surface is constituted by a spherical lattice shell having a triangular network pattern. 2. A circle in which a hemispherical dome is viewed two-dimensionally has a rigidity distribution as uniform as possible and is as close to isotropic as possible, that is, each triangle is as close as possible to an equilateral triangle. The method for constructing a single-layer spherical lattice shell according to claim 1, wherein the method is divided into six equal parts. 3. A circular spherical lattice shell is formed up to the lowermost layer on a fan-shaped main dividing line obtained by dividing a circle into several parts, and the remaining split circle portion is a triangle formed by each lattice member forming the lowermost layer and the ring column position. The method for constructing a single-layer spherical lattice shell according to claim 1, wherein the spherical lattice shell is constructed.