JP2003239388A - Stiffening member layout design method for single-layer lattice shell structure - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a stiffening member layout design method for a single-layer lattice shell structure that can obtain required buckling bearing force with required minimum stiffening and rapidly select stiffened parts. <P>SOLUTION: The in-plane displacement Li and out-of-plane displacement Wi of a joint of each grid g in a single-layer lattice shell in the case of not having a stiffening member are computed. 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. Weight coefficients wi, wo to the in-plane deformation rate γg and out-of-plane deformation rate ψg are respectively determined according to the constraint degree of each grid, and evaluation coefficients κ which are the functions of all or some of selected numeric values of the in-plane deformation rate γg, out-of-plane deformation rate ψg, weight coefficient wi and weight coefficient wo are computed for every grid. Some grids considered to increase buckling load by arranging in-plane stiffening members are selected on the basis of the evaluation coefficients κ, and the in-plane stiffening members are provided for the grids positioned along a line which connects these grids in a shortest distance. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a stiffening member arrangement designing method for a single-layer lattice shell structure used in a frame of various large-scale building structures.

[0002]

2. Description of the Related Art A single-layer lattice shell structure has a single frame structure forming a frame structure, and is a structural type in which a required shell curved surface is formed by a single-layer lattice (planar lattice) without a three-dimensional truss member. is there.

This single-layer lattice shell structure is lighter in weight than the conventional multi-layer truss structure structure, and the joints can be simplified, and not only steel frames but also wood-based materials are structural materials. Since it can be done, etc.
It is being adopted as a framework for lightweight roof membranes in various large-scale building structures, but it has a small bending rigidity and is liable to buckle, so how to increase the resistance to buckling loads is an important point for practical use. Becomes

The buckling load can be expressed as a function of in-plane rigidity and bending rigidity, and as a method of increasing the buckling resistance of a single-layer lattice shell, a lattice structure is combined with another structure to form a hybrid structure. It has been conventionally advocated to increase the internal rigidity and bending rigidity to stiffen the material. As this stiffening, as shown in FIGS. 13 (a), 13 (b) and 14, the grid of the plane truss lattice 2 which is a 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 the 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 the plane, The out-of-plane stiffening shown in FIG. 14 is one in which a post 10 and a cable 8 are incorporated into a plane truss lattice 2 of an unstable quadrangle to form a self-balancing stress type tension stable truss 12 and made into parts.

That is, as shown in FIGS. 15 (a) to 15 (d), the tension-stable truss 12 as this part has two sets of orthogonal cables 8 each of which is composed of two pieces and has a truss main member 2a.
Loosely arranged and connected on the diagonal of the, and the set of cables 8
The post 10 is erected at the midpoint of the cable, and the midpoint of the other set of cables 8 is connected to the upper portion of the post 10. In this way, the post 10 is extended by an expansion / contraction 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 tension device (not shown). Then, the tension is introduced to balance with the compressive force of the truss main material 2a and the post 10 to form the tension-stable truss 12 as a part. The length of the post 10 is set so that the rise / span ratio of the prospective part satisfies the design value based on the extension length calculated in advance based on the tension introduced into the cable 8. In addition to the above assembly, it is also considered that the obtained tension-stable truss 12 is preliminarily attached with a roof membrane 14 such as a steel plate as a secondary member for roof finishing, and the roof membrane 14 is made to function as a load supporting part. There is.

In the single-layer lattice shell having this structure, the tension-stable truss 12 of each part is attached to the truss main material 2
By arranging a in a row so that they are adjacent to each other in a row and column, a single-layer lattice shell having a required curved surface is constructed.

FIG. 16 shows a concrete mounting structure of the tension stabilizing truss 12 as a part to the single-layer lattice shell structure 16. In the figure, a gusset plate 18 for connection is fixed at the intersection of the single-layer lattice shells 16a of the structure 16, and the tension stable truss 1 corresponding to this is fixed.
The gusset plate 20 to be connected to this is fixed to the four sides of 2, and a splice plate (not shown) is applied in a state where they are butted against each other, and these are connected by bolts and nuts, whereby fixing of the tension stable truss 12 is completed.

[0008]

By the way, in the hybrid single-layer lattice shell structure 16 based on the parts system of the tension stable truss 12 described above, the tension stable truss 12 referred to as a part is attached to the single layer lattice shell 16a to provide the in-plane rigidity / proof strength. This structure is to construct a lightweight roof structure by assembling the single-layer lattice shell 16a and then attaching separately assembled parts of the tension-stable truss 12 to all the grids.

However, the tension stable truss 1 for the parts
The cable 8 used as the upper and lower chord members of No. 2 has an accelerating increase in cost when the number of the 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 assembly thereof becomes complicated, and the construction cost becomes expensive.

Therefore, it has been earnestly studied and studied to mount the parts of the tension-stable truss 12 only on a part of the grids, not on all the grids. Abstracts of lectures (Kinki) September 1996 (Research on hybrid single-layer lattice shell by parts method Part 1: Background and goals of research).

That is, in the above research, the buckling mode in the absence of the stiffening material is calculated, and the stiffening material is incorporated in the grid of the twisting mode where the buckling mode is supposed to occur. It is a thing.

However, even if the location where the twist mode is generated is selected and stiffened in this manner, the twist mode changes due to the stiffening, and another location becomes a new location where the twist mode is generated. Therefore, it is necessary to calculate the buckling mode again under the conditions after the stiffening, reconsider whether there is a new twisting mode occurrence point, and repeat this work again and again. There is a risk of waste of stiffening the grids at locations more than necessary with respect to bending strength.

The present invention has been made to solve the above problems, and an object thereof is to improve the buckling resistance of a single-layer lattice shell structure by partially incorporating a stiffening member in the grid. It is an object of the present invention to provide a method of selecting a stiffening member disposition position of a single-layer lattice shell structure, which can perform a minimum necessary stiffening with respect to a required buckling strength and can quickly select a stiffening point. .

[0014]

In order to achieve the above object, the method for designing stiffening members for a single-layer lattice shell structure according to the first aspect of the present invention is a method for designing a single-layer lattice shell for a single-layer lattice shell without a stiffener. The in-plane displacement Li and the out-of-plane displacement Wi of the nodes of the grid g 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 calculated from the out-of-plane displacement Wi. Then, the weighting factors wi and wo for the in-plane deformation rate γg and the out-of-plane deformation rate ψg are determined according to the degree of constraint of each grid, and the in-plane deformation rate γg, the out-of-plane deformation rate ψg, and the weighting factor wi. , And all of the weighting factors wo, or an evaluation coefficient κ, which is a function of some numerical values selected from these, is calculated for each grid, and the in-plane stiffening member is arranged by the evaluation coefficient κ. Increase the buckling load with Select some grids that can be considered as the in-plane stiffening target, and select the grids that are located along the line connecting them with the shortest distance as the in-plane stiffening target, and devise any stiffening member arrangement pattern. The buckling analysis of the hybrid single-layer lattice shell for the arrangement pattern is performed, and the stiffening member arrangement pattern is repeatedly devised until the buckling load in the stiffening member arrangement pattern satisfies the required buckling load. The in-plane stiffening member is provided in a stiffening member arrangement pattern that satisfies the required buckling load.

In the stiffening member layout designing method for a single-layer lattice shell structure according to the first aspect of the present invention, in-plane and out-of-plane deformations are taken into consideration while weighting according to the degree of constraint of the grid. , Quickly determine the optimum placement of stiffening members to obtain a predetermined buckling load, obtain a large buckling load while minimizing the location of stiffening members, and use expensive reinforcement parts The construction cost of the single-layer lattice shell structure can be reduced as much as possible.

In the stiffening member arrangement design method for a single-layer lattice shell structure according to a second aspect of the present invention, the evaluation coefficient κ is
It is characterized in that κ = {(wi · γg) ² + (wo · ψg) ² } ^1/2 . In the stiffening member arrangement designing method for a single-layer lattice shell structure according to the second aspect of the present invention, since a specific mathematical formula is determined, it can be carried out without requiring skill.

In the stiffening member arrangement design method for a single-layer lattice shell structure according to the third aspect of the present invention, the evaluation coefficient κ is
It is characterized in that κ = wi · γg. Claim 3
In the stiffening member arrangement designing method for the single-layer lattice shell structure having the above configuration, since the concrete mathematical formula is simplified, the calculation speed can be increased.

According to a fourth aspect of the present invention, there is provided a stiffening member arrangement design method for a single-layer lattice shell structure, wherein a buckling load of the single-layer lattice shell structure when the stiffening member is incorporated in advance and no stiffening member are provided. In this case, the ratio to the buckling load of the same single-layer lattice shell structure, that is, the supplemental stiffness capability index β is defined, and the specific numerical value of β is determined in designing the single-layer lattice shell structure. The rigid 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 judged whether or not it is adopted depending on whether the specific numerical value of the above β is satisfied. It is characterized in that the stiffening member arrangement pattern is repeatedly devised until a specific numerical value is satisfied. In the stiffening member arrangement design method for a single-layer lattice shell structure having the structure of claim 4, the buckling load sharing between the single-layer lattice shell structure without the stiffening member and the stiffening member is clarified in advance. It is possible to quickly select the disposition position of the stiffening member.

[0019]

Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings. The stiffening member arrangement design method for the single-layer lattice shell structure of the present invention is
The procedure consists of the following (1) to (6). (1) The in-plane displacement Li and the out-of-plane displacement Wi of the nodes of each grid g in the single-layer lattice shell without the stiffening material are calculated. (2) The in-plane deformation rate γg of each grid g is obtained from the in-plane displacement Li obtained in (1) above. (3) The out-of-plane deformation rate ψg of each grid g is obtained from the out-of-plane displacement Wi obtained in (1) above. (4) Weighting coefficient w for the in-plane deformation rate γg obtained in (2) above and the out-of-plane deformation rate ψg obtained in (3) above
i and wo are determined according to each grid position, and κ
= {(Wi · γg) ² + (wo · ψg) ² } ^{1/2 The} evaluation coefficient κ defined by the formula is calculated for each grid g. (5) Select some grids with a large evaluation coefficient κ obtained in (4) above, select grids located along the line connecting them with the shortest distance as in-plane stiffening targets, and select any Create a rigid member placement pattern. (6) Buckling analysis of the hybrid single-layer lattice shell for the stiffening member arrangement pattern is performed until the buckling load in the stiffening member arrangement pattern satisfies the required buckling load,
The above stiffening member arrangement pattern is repeatedly devised to provide the in-plane stiffening member with the stiffening member arrangement pattern that satisfies the required buckling load.

Next, the method for selecting the arrangement position of the stiffening member by these procedures will be described in detail in order.

From the analysis results using various part placement patterns, it is effective to place the parts at locations where the grid deformation of the single-layer lattice shell is large. Can be assumed. Therefore, the buckling mode is used to calculate the in-plane and out-of-plane deformation rates of the grid, and a method for effectively incorporating parts using the following evaluation coefficients will be examined.

--- Definition of design parameters --- The in-plane and out-of-plane deformation rates are defined as follows. The in-plane deformation rate is evaluated (see FIG. 3) using the diagonal change rate γ expressed by the 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) plane To evaluate the outer deformation rate, the main curvature (Equation (3)) at each node
Is calculated using the difference formula. The average value of the four nodes forming the grid is taken 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 The following can be said from analysis examples (FIGS. 1 and 2) using the arrangement patterns of various parts. -Incorporating parts into a grid with large in-plane deformation is effective for increasing the buckling load.・ For both in-plane and out-of-plane deformation, the higher the degree of restraint near the boundary, the higher the buckling load as a shell. Therefore, for each of the in-plane and out-of-plane deformation rates, the weighting factor w determined by the position
By multiplying i and wo, κ represented by the equation (4) is used as the evaluation coefficient. κ = {(wi · γg) ² + (wo · ψg) ² } ^1/2 (4)

---- Study by Calculation Example ---- A model of peripheral pin support and peripheral keel support will be examined. Both models aim at a required buckling load of 2.0 times that of a single layer lattice shell. The value of the weighting factor is set as shown in FIG. 4 in consideration of the above-mentioned phenomenon, and 1 / in consideration of symmetry.
4 parts are shown. Next, the results of using the evaluation coefficient κ are shown in FIGS. 5 to 8. Here, the arrows in the figure show the process of incorporating parts into a large grid of κ.

(A) In the case of peripheral pin support In D-1, as a result of arranging parts on a grid with a large κ in consideration of continuity with the boundary, the required buckling load was reached in one examination. , Indicating the effectiveness of using κ. Next, in B-1, parts are incorporated at 32 places to increase the buckling load. Furthermore, the required buckling load is reached by incorporating parts at 16 locations based on the value of κ. This is considered to be due to the stiffening effect of the parts being continuous in addition to the stiffening effect of the individual parts.
It is shown that the effectiveness by the continuity of parts can be evaluated together by the examination using. On the other hand, the arrangement of C-2 was not effective, and the improvement was aimed at by κ, but it was not effective because there was no overall continuity of parts. Therefore, in the rectangular plane single-layer lattice EP shell structure in which the outer peripheral portion is pin-supported, as shown in FIG. 10, for example, the single-layer lattice shell structure 1 based on the arrangement selection of D-1 in FIG.
In each side 16A-D of the outer peripheral portion as a whole of 6, the grids located along the line connecting the respective midpoints 16Am, 16Bm, 16Cm, 16Dm to each other are attached to the surface of the tension stable truss 12 or the like. A rectangular planar hybrid single layer lattice EP shell structure having a structure incorporating an internal stiffening member becomes effective.

(B) In the case of supporting the peripheral keel, the parts of C-2 were arranged at 16 positions including the position showing the maximum value of κ, but the increase of the buckling load was small. As a result of arranging the parts considering the continuity to the boundary support point, the required buckling load was reached. In contrast, A-1 and D-1 in which parts were arranged at 32 positions did not show effective results. Here, A-
In No. 2, the required buckling load is obtained. This is also considered to be a stiffening effect due to the continuity of 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 makes 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 the effective arrangement of parts. In addition to the stiffening effect of the part itself, the stiffening effect due to the continuity of the part and the continuity to the boundary support points is large, and the value of κ is large when incorporating the part, and the above continuity is satisfied. It is important to think together. Therefore, in the rectangular plane hybrid single layer lattice EP shell structure in which the outer periphery is keel supported, for example, based on the arrangement selection of C-3 in FIG.
As shown in FIG. 11, a rectangular flat hybrid single-layer lattice EP shell structure having a structure in which an in-plane stiffening member such as a tension stable truss 12 is incorporated in a grid located along the diagonal line of the single-layer lattice shell structure 16 is effective. It will be Further, as shown in FIG. 12, the stiffening member is not limited to the tension stable truss, and may be a plate member such as a steel plate.

A design flow for a buckling load of a hybrid single-layer lattice shell using this method is shown in FIG. 9 as common to the case of supporting peripheral pins and the case of supporting peripheral keels. As shown in the figure, first, after setting the required buckling load P _n of the hybrid single-layer lattice shell, a buckling analysis of the single-layer lattice shell is performed to set the buckling load _s P _cr of the single-layer lattice shell. To do. Next, the index β is set and the stiffening parts are designed. Index β here
Is the buckling load P of a single-layer lattice shell (hybrid single-layer lattice shell) structure when a stiffening member is incorporated.
_It is the ratio of _n and the buckling load _s P _cr of the same single layer lattice shell structure without stiffening member, which controls the sharing of the buckling load between the lattice shell and the stiffening part. Design the layout of parts to meet the requirements. 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 stiffening members in all grids.

In the layout design of the parts, the deformation rate of each grid of the single-layer lattice shell is calculated by the above equations (1) to (3), and the evaluation coefficient κ is calculated by the above equation (4). Then, select some grids with a large evaluation coefficient κ, select grids located along the line connecting them with the shortest distance as in-plane stiffening targets, and devise any stiffening member arrangement pattern, Assuming that parts are incorporated in the pattern, buckling load is calculated by performing buckling analysis of the hybrid single layer lattice shell for each stiffening member arrangement pattern.
_H P _cr is calculated to determine whether or not the specific value of β is satisfied, that is, the required necessary buckling load P _n is P _n ≦ _H P _cr
= Β _s · P _cr It is judged whether or not it is adopted depending on whether it is satisfied, if it is satisfied, it is decided as OK, and if it is not satisfied, it is decided as NG by repeating the arrangement design of the parts until it becomes OK. Determine the placement pattern.

Further, by using this index β,
Regardless of whether or not the evaluation coefficient κ is used, the selection of the arrangement position can be speeded up.

[0031]

As described in detail above, the method of selecting the stiffening member disposition position of the single-layer lattice shell structure according to the present invention has the following excellent effects.

In the stiffening member arrangement design method for a single-layer lattice shell structure according to the first aspect of the present invention, since the deformation in the in-plane and out-of-plane directions is taken into consideration while performing weighting according to the degree of constraint of the grid, The optimal placement of stiffening members to obtain the buckling load can be quickly determined, a large buckling load can be obtained, and expensive reinforcing parts can be effectively used while minimizing the location of stiffening members. The construction cost of the single-layer lattice shell structure can be reduced as much as possible.

In the stiffening member arrangement designing method for a single-layer lattice shell structure according to the second aspect of the invention, since a specific mathematical formula is determined, it can be carried out without requiring skill.

In the stiffening member arrangement design method for the single-layer lattice shell structure having the structure of the third aspect, since the specific mathematical formula is simplified, the calculation speed can be increased.

In the stiffening member arrangement design method for a single-layer lattice shell structure according to the fourth aspect of the present invention, the sharing of buckling strength between the single-layer lattice shell structure without the stiffening member and the stiffening member is clarified in advance. By doing so, the placement position of the stiffening member can be quickly selected.

[Brief description of drawings]

FIG. 1 is a comparison diagram of buckling modes of peripheral pin support models.

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

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

FIG. 4 is a diagram illustrating an example of how to give a weighting coefficient to a grid.

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

FIG. 6 is a diagram for explaining transition of κ for each grid due to incorporation of parts in the case of supporting peripheral pins.

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

FIG. 8 is a diagram for explaining transition of κ for each grid due to incorporation of parts in the case of supporting a peripheral keel.

FIG. 9 is a design flow chart showing the procedure of a stiffening member arrangement design method for a single-layer lattice shell structure according to the present invention.

FIG. 10 is a plan view showing an example in which a stiffening member is attached to a preferable position for a rectangular flat single-layer lattice EP shell structure supporting peripheral pins.

FIG. 11 is a plan view showing an example in which a stiffening member is attached to a preferable position for a rectangular flat single-layer lattice EP shell structure supporting a peripheral keel.

FIG. 12 is a cross-sectional view taken along the line aa in FIG.

13A and 13B are diagrams showing 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.

15A to 15D are explanatory views showing a process of assembling parts.

FIG. 16 is an explanatory diagram 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 posts 12 Tension stable truss (parts) 14 roof membrane 16 Single-layer lattice shell structure 18,20 Gusset plate

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Kei Kanayama             Osaka Prefecture Osaka City Chuo-ku Kitahama East 4-33 shares             Company Obayashi Head Office

Claims (4)

[Claims] 1. An in-plane displacement Li and an out-of-plane displacement W of a node of each grid g in a single-layer lattice shell without a stiffener.
i and the in-plane deformation rate γg of each grid from the in-plane displacement Li, and the out-of-plane deformation rate ψg of each grid from the out-of-plane displacement Wi.
Then, the weighting factors wi and wo for the in-plane deformation rate γg and the out-of-plane deformation rate ψg are determined according to the degree of constraint of each grid, and the in-plane deformation rate γg, the out-of-plane deformation rate ψg, and the weighting coefficient are determined. w
i and all of the weighting factors wo, or an evaluation coefficient κ that is a function of some numerical values selected from these
For each grid, select some grids that can be considered to increase the buckling load by arranging in-plane stiffening members with the evaluation coefficient κ, and position them along the line connecting them with the shortest distance. A grid to be stiffened is selected as an in-plane stiffening target, an arbitrary stiffening member arrangement pattern is devised, buckling analysis of the hybrid single-layer lattice shell for the stiffening member arrangement pattern is performed, and the stiffening member arrangement pattern is selected. The stiffening member arrangement pattern is repeatedly devised until the buckling load in step S4 satisfies the required buckling load, and the in-plane stiffening member is provided in the stiffening member arrangement pattern satisfying the required buckling load. A design method for stiffening members of a single-layer lattice shell structure, characterized by the above. 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 layout design method. 3. The stiffening member arrangement design method for a single-layer lattice shell structure according to claim 1, wherein the evaluation coefficient κ is κ = wi · γg. 4. The ratio of the buckling load of a single-layer lattice shell structure when a stiffening member is incorporated in advance to the buckling load of the same single-layer lattice shell structure without a stiffening member, that is, Define the stiffness index β, determine the specific value of β when designing the single-layer lattice shell structure,
On the other hand, devise an arbitrary stiffening member arrangement pattern, calculate the buckling load of the single-layer lattice shell for each stiffening member arrangement pattern, and judge whether to adopt it depending on whether the specific value of β above is satisfied Then, the stiffening member arrangement pattern is repeatedly devised until the specific value of β is satisfied, wherein the stiffening member arrangement design method for a single-layer lattice shell structure is characterized.