JP2000087447A - Method for selecting placement position of stiffening member for single-latticed shell structure and rectangular planar hybrid single-latticed ep shell structure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for selecting the placement position of a stiffening member for a single-latticed shell structure, whereby the required buckling resistance can be obtained from required minimum stiffening and a portion to be stiffened can be selected rapidly. SOLUTION: The in-plane displacement Li and the out-of-plane displacement Wi of the joint of each grid (g) in a single-latticed shell without stiffeners are calculated to determine the in-plane deformation rate γg of each grid from the in-plane displacement Li and to determine the out-of-plane deformation rate ψg of each grid from the out-of-plane displacement Wi. Weighting functions wi, wo for the in-plane deformation rate γg and the out-of-plane deformation rate ψg, respectively, are defined to match the degree of restraint of each grid. An evaluation coefficient κ, which is a function of numerical values for all or some of the in-plane deformation rate γg, the out-of-plane deformation rate ψg, the weighting function wi, and the weighting function wo, is calculated for each grid. Some of the grids that can be regarded as increasing buckling load by placing in-plane stiffening members are selected on the basis of the evaluation coefficient κ, and the in-plane stiffening members are provided for the grids situated along a line connecting the grids by the shortest distance.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for selecting a stiffening grid position of a single-layer lattice shell structure used for frames of various large-scale building structures, and a stiffening material incorporated in some of the grids for hybridization. The present invention relates to a rectangular planar hybrid single-layer lattice EP shell structure.

[0002]

2. Description of the Related Art A single-layer lattice shell structure is a structure in which a required shell curved surface is formed by a single-layer lattice (plane lattice) having no three-dimensional truss members, which has a single frame forming a frame structure. is there. This single-layer lattice shell structure
Compared to the conventional multi-layer truss structure, it is lighter,
Since it is possible to simplify joints, etc., and not only steel frames but also wood-based materials can be used as structural materials, it has attracted attention in recent years and is being used as a framework for lightweight roof membranes in various large building structures. However, there is a surface with low bending stiffness and easy buckling, and how to increase the proof stress against buckling load is an important point in practical use.

Here, the buckling load can be expressed as a function of in-plane rigidity and bending rigidity. One method of increasing the buckling resistance of a single-layer lattice shell is to combine a lattice shell with another structure to form a hybrid structure. Conventionally, it has been advocated to increase internal rigidity and bending rigidity to stiffen. As the stiffening, as shown in FIGS. 13A, 13B and 14, the grid of the plane truss lattice 2 forming the basic element is
There are in-plane stiffening (FIG. 13) in which the cable 4, the membrane, the steel plate 6 and the like are arranged in a plane, and out-of-plane stiffening (FIG. 14) in which the post 10, the cable 8, the membrane and the like are arranged out of plane. The out-of-plane stiffening shown in FIG. 14 is obtained by incorporating a post 10 and a cable 8 into an unstable quadrilateral plane truss lattice 2 to form a self-balancing stress type tension stable truss 12, and forming parts.

More specifically, as shown in FIGS. 15 (a) to 15 (d), a tension-stable truss 12 as this part is constructed by connecting two sets of orthogonal cables 8 each composed of two truss main members 2a.
Loosely arranged and connected on the diagonal of
The post 10 is erected at the midpoint of the cable 10 and the midpoint of another set of cables 8 is connected to the top of the post 10. Then, the post 10 is extended by a telescopic mechanism such as a screw mechanism (not shown) incorporated in the post 10, or tightened by a turnbuckle (not shown) incorporated in the cable 8, or the cable 8 is tensioned by a hydraulic tensioning device (not shown). Then, tension is introduced to balance with the compressive force of the truss main member 2a and the post 10, thereby forming the tension stable truss 12 as a part. The length of the post 10 is set so that the rise-span ratio of the part satisfies the design value, based on the elongation length calculated in advance based on the introduction tension of the cable 8. In addition to the above assembly, it is also considered that a roof membrane 14 such as a steel plate is previously attached to the obtained tension stable truss 12 as a secondary member for roof finishing, and the roof membrane 14 functions as a load supporting part. I have.
In the single-layer lattice shell of this structure, the tension-stable truss 12 of each part is arranged in a row in the vertical and horizontal directions with the truss main members 2a adjacent to each other, thereby constructing a single-layer lattice shell frame having a required curved surface. I do.

FIG. 16 shows a specific mounting structure of the tension stable truss 12 as a part to the single-layer lattice shell structure 16. In the figure, a connecting gusset plate 18 is fixed at the intersection of each single-layer lattice shell 16a of the structure 16, and the tension-stable truss 1 is
A gusset plate 20 to be connected to the gusset plate 20 is fixed to the four sides of No. 2 and a splice plate (not shown) is applied in a state where the two are butted together, and these are connected by bolts and nuts.

[0006]

By the way, in the hybrid single-layer lattice shell structure 16 of the tension-stable truss 12 using the parts system, the tension-stable truss 12 called a part is attached to a single-layer lattice shell 16a, and rigidity and proof stress in and out of the plane are provided. In this structure, after assembling the single-layer lattice shell 16a, the separately assembled parts of the tension stable truss 12 are attached to all the grids to construct a lightweight roof structure.

[0007] However, the part tension stable truss 1
As for the cable 8 used as the upper and lower chord members, the cost increases at an accelerating rate when the number of gussets 20 of the end fittings increases. That is, since the cable 8 is cut for each part, the number of the cables 8 increases, the assembling thereof becomes complicated, and the construction cost increases. Therefore, instead of attaching the parts consisting of the tension stable truss 12 to all grids,
To be installed only in some grids,
It is being studied and studied diligently [Referred to the Architectural Institute of Japan, Abstracts of Academic Lectures (Kinki), September 1996 (Study on Hybrid Single-Layer Lattice Shell by Part Method, Part 1: Research Background and Goals)]. That is, in the above research, the buckling mode in the case where there is no stiffener is calculated, and the stiffener is incorporated in the grid at the place where the buckling mode is assumed to occur. .

However, even if the location where the torsional mode is generated is selected and stiffened in this way, the stiffening changes the torsional mode and another location becomes a new location where the torsional mode is generated. Therefore, it is necessary to calculate the buckling mode again under the conditions after the stiffening and to examine again whether there is a place where a new torsion mode occurs, and to repeat this work many times. There is a possibility that the grid may be wastefully stiffened at a location more than necessary with respect to the bending strength.

The present invention has been made to solve the above problems, and an object thereof is to improve the buckling strength of a single-layer lattice shell structure by incorporating a stiffening member partially in a grid. A method of selecting a stiffening member disposing position of a single-layer lattice shell structure, which can minimize a necessary stiffening for a required buckling strength and can quickly select a stiffening portion, and some grids It is an object of the present invention to provide a rectangular flat single-layer lattice EP shell structure which stiffens the minimum required.

[0010]

In order to achieve the above object, a method of selecting a stiffening member disposing position of a single-layer lattice shell structure according to the present invention is provided by a single-layer lattice shell having no stiffener. In-plane displacement L of the node of each grid g at
i and the out-of-plane displacement Wi are calculated, the in-plane deformation rate γg of each grid is obtained from the in-plane displacement Li, and the out-of-plane deformation rate ψg of each grid is obtained from the out-of-plane displacement Wi.
Weighting functions wi and wo for g and the out-of-plane deformation rate ψg are respectively determined according to the degree of constraint of each grid, and among the in-plane deformation rate γg, out-of-plane deformation rate ψg, weight function wi, and weight function wo, Is calculated for each grid, and the buckling load is increased by arranging the in-plane stiffening member according to the evaluation coefficient κ. It is characterized in that some grids that can be regarded as are selected, and an in-plane stiffening member is provided for a grid located along a line connecting them at the shortest distance.

In the method for selecting a stiffening member disposing position of a single-layer lattice shell structure according to the first aspect of the present invention, the deformation in the in-plane and out-of-plane directions is considered while performing weighting according to the degree of constraint of the grid. As a result, it is possible to quickly determine the optimum arrangement of the stiffening members to obtain a predetermined buckling load, and to obtain a large buckling load while minimizing the arrangement of the stiffening members, thereby increasing the cost of reinforcing parts. Can be effectively used, and the construction cost of the single-layer lattice shell structure can be reduced as much as possible.

According to a second aspect of the present invention, there is provided the method for selecting a stiffening member disposing position of a single-layer lattice shell structure, wherein the evaluation coefficient κ
Κ = {(wi · γg) ² + (wo · {g) ² }
It is ^1/2, and wherein the.

[0013] In the method for selecting a stiffening member disposing position of a single-layer lattice shell structure having the structure of the second aspect, since a specific mathematical expression is determined, it can be performed without skill.

According to a third aspect of the present invention, there is provided a method for selecting a stiffening member disposing position of a single-layer lattice shell structure, wherein the evaluation coefficient κ
Is κ = wi · γg.

In the method for selecting a stiffening member disposing position for a single-layer lattice shell structure according to the third aspect of the present invention, since specific mathematical expressions are simplified, the calculation speed can be increased.

According to a fourth aspect of the present invention, there is provided a method for selecting a stiffening member disposing position of a single-layer lattice shell structure, comprising the steps of: The ratio with the buckling load of the same single-layer lattice shell structure in the absence of, that is, the stiffness capacity index β is defined, and in designing the single-layer lattice shell structure, a specific numerical value of β is determined. Devising a stiffening member arrangement pattern, calculating the buckling load of the single-layer lattice shell for each stiffening member arrangement pattern, and determining whether or not to adopt the specific value of the above β to determine whether to adopt. Features.

According to the fourth aspect of the present invention, in the method for selecting a stiffening member disposing position of a single-layer lattice shell structure, the buckling resistance sharing between the single-layer lattice shell structure having no stiffening member and the stiffening member is performed in advance. By clarifying, the arrangement position of the stiffening member can be quickly selected.

Here, according to the method of selecting the stiffening position,
As shown in the invention according to claim 5, in a rectangular flat single-layer lattice EP shell structure whose outer peripheral portion is supported by a pin,
A rectangular planar hybrid single-layer lattice EP shell structure having a configuration in which an in-plane stiffening member is incorporated in a grid positioned along a line connecting the midpoints of adjacent sides of the structure periphery can be obtained.

According to the above-mentioned method of selecting a stiffening position, a rectangular plane single-layer lattice E having an outer peripheral portion supported by a keel and four corners supported by pins is provided, as shown in the invention of claim 6.
In the P-shell structure, it is possible to obtain a rectangular flat hybrid single-layer lattice EP shell structure in which an in-plane stiffening member is incorporated in a grid located along a diagonal line of the P-shell structure.

[0020]

Preferred embodiments of the present invention will be described below in detail with reference to the accompanying drawings. The method for selecting the stiffening member disposition position of the single-layer lattice shell structure of the present invention comprises the following procedures (1) to (5). (1) Calculate the in-plane displacement Li and the out-of-plane displacement Wi of the node of each grid g in the single-layer lattice shell without a stiffener. (2) The in-plane deformation rate γg of each grid g is obtained from the in-plane displacement Li obtained in (1). (3) The out-of-plane deformation rate Δg of each grid g is obtained from the out-of-plane displacement Wi obtained in (1). (4) A weighting function w for the in-plane deformation rate γg obtained in (2) and the out-of-plane deformation rate ψg obtained in (3)
i and wo are determined according to each grid position, and κ
= {(Wi · γg) ² + (wo · Δg) ² } An evaluation coefficient κ defined by an equation of ^1/2 is calculated for each grid g. (5) Several grids with large evaluation coefficients κ obtained in (4) are selected, and grids located along a line connecting them at the shortest distance are selected as in-plane stiffening targets. Next, a method for selecting the disposition position of the stiffening member in these procedures will be described in detail step by step.

------ Selection method of arrangement of stiffening parts --- From analysis results using arrangement patterns of various parts, it is effective to arrange parts at locations where the grid deformation of the single-layer lattice shell is large. Can be assumed. Therefore, the in-plane and out-of-plane deformation rates of the grid are calculated using the buckling mode, and a method of effectively incorporating parts using the following evaluation coefficients is examined.

--- Definition of design parameters --- In-plane and out-of-plane deformation rates are defined as follows. The evaluation of the in-plane deformation rate (see FIG. 3) is performed using the diagonal change rate γ represented by equation (1). _{γ 1 = (L'ik-Lik} ) / Lik ......... (1) γ 2 = (L'jl-Ljl) / Ljl γg = (γ 1 2 + γ 2 2) 1/2 ......... (2) surface For the evaluation of the outside deformation rate, the principal curvature at each node (Equation (3))
Is calculated using the difference formula. The average value of the four nodes forming the grid is defined as the grid evaluation value. ψi = (∂ ² Wi / ∂x ² ) + (∂ ² wi / ∂y ² ) (3) where Wi: deflection in the out-of-plane direction Proposal of evaluation coefficient κ Various arrangement patterns of parts are used. The following can be said from the analysis examples (FIGS. 1 and 2). -Incorporating parts into a grid with large in-plane deformation is effective in increasing buckling load. -For both in-plane and out-of-plane deformation, the higher the degree of constraint near the boundary, the higher the buckling load of the shell. Therefore, the weight function w determined by the position is given to each of the in-plane and out-of-plane deformation rates.
By multiplying i and wo, κ represented by equation (4) is set as an evaluation coefficient. κ = ｛(wi · γg) ² + (wo · ψg) ^{2 １ ／ 1/2} (4)

--- Study by Calculation Example-- A model of peripheral pin support and peripheral keel support will be examined. Both models target the required buckling load to be 2.0 times that of a single-layer lattice shell. The value of the weighting function is determined as shown in FIG.
4 parts are shown. Next, results using the evaluation coefficient κ are specifically shown in FIGS. Here, the arrows in the figure show the process of assembling parts into a grid with a large κ.

(A) In the case of peripheral pin support In D-1, the parts were arranged on the grid having a large κ in consideration of the continuity with the boundary, and as a result, the required buckling load was reached in one examination. And shows the effectiveness of using κ. Next, in B-1, parts are incorporated in 32 places to increase the buckling load. Furthermore, the required buckling load has been reached by incorporating parts at 16 locations based on the value of κ. This is thought to be due to the stiffening effect of the continuation of parts added to the stiffening effect of the parts alone, and κ
The results show that the effectiveness due to the continuity of parts can also be evaluated. On the other hand, the arrangement of C-2 was not effective and aimed at improvement by κ, but was not effective due to lack of overall continuity of parts. Therefore, in a rectangular flat single-layer lattice EP shell structure whose outer peripheral portion is supported by pins, as shown in FIG. 10 based on, for example, the selection of the arrangement of D-1 in FIG.
6, a grid such as a tension-stable truss 12 is provided on a grid located along a line connecting adjacent midpoints 16Am, 16Bm, 16Cm, and 16Dm of each side 16A to 16D of the outer peripheral portion as a whole. A rectangular planar hybrid single-layer lattice EP shell structure having a structure incorporating an internal stiffening member is effective.

(B) Case of Supporting Peripheral Keel C-2 has parts arranged at 16 positions including the position showing the maximum value of κ, but the rise in buckling load was small. The required buckling load was reached as a result of arranging the parts in consideration of the continuity to the boundary support points. In contrast, A-1 and D-1 in which parts were arranged at 32 locations did not show effective results. Here, A-
2, the required buckling load is obtained. This is also considered to be a stiffening effect due to the continuity between the parts and the boundary support points. C
By comparing -3 and D-1, when incorporating parts,
It can be seen that the difference in the boundary conditions causes a great difference in the effect of incorporating the parts. From the above examination, it was confirmed that the method of examining the arrangement of parts using the evaluation coefficient κ based on the deformation rate of the single-layer lattice shell is effective in determining an effective arrangement of parts.

In addition to the stiffening effect of the parts alone, the stiffening effect due to the continuity of the parts and the continuity to the boundary support points is large, and when the parts are incorporated, the value of κ is large. It is important to consider that the conditions are satisfied. Therefore, in a rectangular flat hybrid single-layer lattice EP shell structure in which the outer periphery is keel-supported, for example, based on the layout selection of C-3 in FIG.
As shown in the figure, a rectangular flat hybrid single-layer lattice EP shell structure having a configuration in which an in-plane stiffening member such as a tension-stable truss 12 is incorporated in a grid located along a diagonal line of the single-layer lattice shell structure 16 is effective. Becomes Further, as shown in FIG. 12, the stiffening member is not limited to a tension-stable truss, but may be a plate-like member such as a steel plate.

FIG. 9 shows a design flow for the buckling load of the hybrid single-layer lattice shell using this method, which is common to the case of supporting the peripheral pin and the case of supporting the peripheral keel. Here, the index β is a ratio of the buckling load of the single-layer lattice shell structure when the stiffening member is incorporated to the buckling load of the same single-layer lattice shell structure without the stiffening member, And the buckling load of the stiffening parts is controlled, and the layout of the parts is designed to satisfy this. The index β is preferably in the range of 2.0 to 5.0. When β = 5.0, there is a high possibility that it becomes necessary to incorporate a stiffening member into all grids. Further, by using the index β, it is possible to speed up the selection of the arrangement position regardless of whether the evaluation coefficient κ is used.

[0028]

As described in detail above, the method for selecting the position of the stiffening member of the single-layer lattice shell structure according to the present invention has the following excellent effects. In the method for selecting a stiffening member disposition position of a single-layer lattice shell structure according to the first aspect, a predetermined seat is used in order to take into account in-plane and out-of-plane deformation while performing weighting according to the degree of grid constraint. It is possible to quickly determine the optimal arrangement of stiffening members to obtain buckling loads, obtain a large buckling load while minimizing the location of stiffening members, and effectively use expensive reinforcing parts, The construction cost of the single-layer lattice shell structure can be reduced as much as possible.

In the method for selecting a stiffening member disposing position for a single-layer lattice shell structure according to the second aspect of the present invention, since specific mathematical expressions are determined, the method can be performed without skill.

In the method for selecting a stiffening member disposing position for a single-layer lattice shell structure according to the third aspect of the present invention, the specific mathematical expressions are simplified, so that the calculation speed can be increased.

According to the fourth aspect of the present invention, in the method for selecting a stiffening member disposing position of a single-layer lattice shell structure, the buckling resistance sharing between the single-layer lattice shell structure without the stiffening member and the stiffening member is performed in advance. By clarifying, the arrangement position of the stiffening member can be quickly selected.

Here, according to the method of selecting the stiffening position,
In the rectangular flat hybrid single-layer lattice EP shell structure whose outer peripheral portion is supported by a pin as set forth in the invention according to claim 5, a position is set along a line connecting midpoints of adjacent sides of the peripheral edge of the structure. Thus, it is possible to quickly obtain a rectangular flat hybrid single-layer lattice EP shell structure having a configuration in which an in-plane stiffening member is incorporated in a grid.

According to the above-mentioned method of selecting a stiffening position, a rectangular flat hybrid single-layer lattice EP shell structure in which the outer peripheral portion is keel-supported and the four corners are pin-supported as described in the invention according to claim 6. In the above, a rectangular flat hybrid single-layer lattice EP shell structure having a configuration in which an in-plane stiffening member is incorporated in a grid located along a diagonal line of the structure can be obtained quickly.

[Brief description of the drawings]

FIG. 1 is a comparison diagram of a buckling mode of a peripheral pin support model.

FIG. 2 is a comparison diagram of a buckling mode of a peripheral keel support model.

FIG. 3 is an explanatory diagram of evaluation of an in-plane deformation rate.

FIG. 4 is a diagram illustrating an example of how to assign a weight coefficient to a grid;

FIG. 5 is a diagram illustrating a transition of a buckling load for each grid due to the incorporation of parts in the case of peripheral pin support.

FIG. 6 is a diagram illustrating a transition of κ for each grid by incorporating parts in the case of supporting peripheral pins.

FIG. 7 is a diagram illustrating a transition of a buckling load for each grid due to the incorporation of parts in the case of supporting a peripheral keel.

FIG. 8 is a diagram illustrating a transition of κ for each grid by incorporating parts in the case of supporting a peripheral keel.

FIG. 9 is a design flowchart showing a procedure of a method for selecting a stiffening member arrangement position of a single-layer lattice shell structure of the present invention.

FIG. 10 is a plan view showing an example in which a stiffening member is assembled at a preferred position with respect to a rectangular flat single-layer lattice EP shell structure supporting a peripheral pin.

FIG. 11 is a plan view showing an example in which a stiffening member is assembled at a preferred position with respect to a rectangular flat single-layer lattice EP shell structure supporting a peripheral keel.

FIG. 12 is a sectional view taken along the line aa in FIG. 26;

13A and 13B are diagrams illustrating an example of in-plane stiffening.

FIG. 14 is an explanatory diagram of a tension stable truss showing an example of out-of-plane stiffening.

FIGS. 15A to 15D are explanatory diagrams showing a part assembling process.

FIG. 16 is an explanatory view showing a specific example of a structure for attaching a tension stable truss to a single-layer lattice shell.

[Explanation of symbols]

 2 Plane truss 2a Truss main material 4,8 Cable 6 Steel plate 10 Post 12 Tension stable truss (parts) 14 Roof membrane 16 Single layer lattice shell structure 18,20 Gusset plate

 ──────────────────────────────────────────────────続 き Continued on the front page F term (reference) 2E125 AA42 AB13 AC18 AG20 BB09 BC09 BD01 BE02 BF03 BF08 CA05 CA15 2E163 FA01 FA09 FB06 FB32

Claims (6)

[Claims] 1. An in-plane displacement Li and an out-of-plane displacement W at a node of each grid g in a single-layer lattice shell without a stiffener.
i, an in-plane deformation rate γg of each grid is obtained from the in-plane displacement Li, and an out-of-plane deformation rate ψg of each grid is obtained from the out-of-plane displacement Wi.
The weighting functions wi and wo for the in-plane deformation rate γg and the out-of-plane deformation rate ψg are respectively determined according to the degree of constraint of each grid, and the above-mentioned in-plane deformation rate γg, out-of-plane deformation rate ψg, w
i, and an evaluation coefficient κ which is a function of all of the weight functions wo or some numerical value selected from these.
Is calculated for each grid, and several grids that can be considered to increase the buckling load by arranging the in-plane stiffening members based on the evaluation coefficient κ are selected, and the positions along the line connecting them at the shortest distance are selected. An in-plane stiffening member is provided for a grid to be formed, and a stiffening member disposition position selecting method for a single-layer lattice shell structure is provided. 2. The single-layer lattice shell structure according to claim 1, wherein the evaluation coefficient κ is κ = ｛(wi · γg) ² + (wo · ψg) ² ｝ ^1/2 . Stiffening member arrangement position selection method. 3. The method according to claim 1, wherein the evaluation coefficient κ is κ = wi · γg. 4. The ratio between the buckling load of a single-layer lattice shell structure in which a stiffening member is incorporated in advance and the buckling load of the same single-layer lattice shell structure in the absence of a stiffening member, Define the stiffness index β, determine the specific numerical value of β in the design of a single-layer lattice shell structure,
On the other hand, an arbitrary stiffening member arrangement pattern is devised, the buckling load of the single-layer lattice shell for each stiffening member arrangement pattern is calculated, and it is determined whether or not to adopt the specific value of β described above. A stiffening member disposing position selecting method for a single-layer lattice shell structure. 5. A rectangular planar single-layer latticed EP shell structure whose outer peripheral portion is supported by a pin. In-plane stiffening is performed on a grid located along a line connecting midpoints of adjacent sides of the peripheral edge of the structure. A rectangular planar hybrid single-layer lattice EP shell structure comprising a member incorporated therein. 6. A rectangular planar single-layer lattice EP shell structure in which an outer peripheral portion is keel-supported and four corners are pin-supported, and an in-plane stiffening member is incorporated in a grid located along a diagonal line of the structure. A rectangular planar hybrid single layer lattice EP shell structure characterized by the following: